Polynomials

CBSE Class 10 Mathematics · every board question from this chapter, 2023–2026

• If the zeroes of a polynomial p(x) are -3 and 8, then p(x) equals2026
• The graph of y=f(x) is given. The number of distinct zeroes of y=f(x) is:2026
• The graph of y=f(x) is given. The number of zeroes of f(x) is:2026
• Observe the graph of polynomial p(x). Number of zeroes of p(x) is2026
• If α and β are two zeroes of a polynomial f(x)=px^2-2 x+3 p and α+β=α β, then value of p is:2026
• A polynomial p(x), which has sum of its zeroes equal to their product, is:2026
• Observe the graph of polynomial p(x). The zeroes of the polynomial are2026
• How many zeroes does p(x)=(x-2)(x+3) have?2026
• If sum and product of zeroes of a polynomial are (-3) and (-2) respectively, then a polynomial is2026
• The sum and product of zeroes of a quadratic polynomial p(x) are -1/3 and 2 respectively. The polynomial p(x) is:2026
• Assertion: The polynomial p(y)=y^2+4 y+3 has two zeroes. Reason (R): A quadratic polynomial can have at most two zeroes.2026
• If α, β are the zeroes of the polynomial p(x)=x^2-3 x-1, then find the value of 1/(α)+1/(β).2026
• If α, β are the zeroes of the quadratic polynomial px^2+qx+r, then find the value of α^3 β+β^3 α.2026
• α, β are zeroes of the polynomial p(x)=3 x^2-6 x-5. Find the value of 1/(α^2)+1/(β^2).2026
• Find the value of p, for which one zero of the quadratic polynomial px^2-14 x+8 is 6 times the other.2026
• Find a quadratic polynomial whose zeroes are (5-2 √3) and (5+2 √3).2026
• α and β are the zeroes of the polynomial 5 x^2-16 x-10. Find the value of (α)/(β)+(β)/(α).2026
• Find the zeroes of the quadratic polynomial x^2+7 x+10, and verify the relationship between the zeroes and its coefficients.2026
• During a theatre drama, a backdrop of building arches was used. The shape of the curve shown below can be represented by the…2026
• An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills…2026
• The quadratic equation whose sum and product of roots are 'a' and ' 1/a, respectively is:2025
• If α and β are the zeroes of polynomial 3 x^2+6 x+k such that α+β+α β=-2/3, then the value of k is:2025
• The quadratic equation whose roots are 7 and 1/7 is:2025
• If α and β are the zeroes of the polynomial p(x)=x^2-a x-b, then the value of (α+β+α β) is equal to:2025
• If the zeroes of the polynomial a x^2+b x+(2 a)/b are reciprocal of each other, then the value of b is2025
• If α and β are zeroes of the polynomial p(x)=kx^2-30 x+45 k and α+β=α β, then the value of 'k' is:2025
• If one zero of the polynomial q(x)=(p^2+4) x^2+65 x+4 p is reciprocal of the other, then the value of ' p ' is:2025
• Zeroes of the polynomial p(y)=7 y^2-11/3 y-2/3 are:2025
• Two polynomials are shown in the graph below. The number of distinct zeroes of both the polynomials is:2025
• The sum of the zeroes of the polynomial p(x)=5 x-7 x^2+3 is:2025
• If - 4 is a zero of the polynomial p(x)=x^2-x-(2+2 k), then the value of k is:2025
• Zeroes of the polynomial p(x)=x^2-3 √2 x+4 are:2025
• Which of the following statements is true for a polynomial p(x) of degree 3?2025
• Find a quadratic polynomial whose zeroes are 2 and -7/5.2025
• If the sum of the zeroes of the polynomial p(x)=(p+1) x^2+(2 p+3) x+(3 p+4) is -1, then find the value of 'p'. OR If α and β are…2025
• If the zeroes of the polynomial x^2+ax+b are in the ratio 3: 4, then prove that 12 a^2=49 b.2025
• If p and q are zeroes of the polynomial p(y)=21 y^2-y-2, then find the value of (1-p).(1-q).2025
• Find the zeroes of the polynomial p(x)=x^2+4/3 x-4/3.2025
• α and β are zeroes of a quadratic polynomial x^2-a x-b. Obtain a quadratic polynomial whose zeroes are 3 α+1 and 3 β+1.2025
• Find the zeroes of the polynomial p(x)=6 x^2-5 x-1. Hence, obtain a polynomial each of whose zeroes is three times the zeroes of…2025
• Obtain the zeroes of the polynomial 7 x^2+18 x-9. Hence, write a polynomial each of whose zeroes is twice the zeroes of given…2025
• Find the zeroes of the polynomial p(x)=3 x^2-4 x-4. Hence, write a polynomial whose each of the zeroes is 2 more than zeroes of…2025
• If α and β are the zeroes of the polynomial a x^2-x+c. Obtain a polynomial whose zeroes are α-3 and β-3.2025
• Obtain the zeroes of the polynomial p(x)=2 x^2-5 x-3. Hence, obtain a polynomial each of whose zeroes is one less than each of…2025
• Find the zeroes of the polynomial q(x)=8 x^2-2 x-3. Hence, find a polynomial whose zeroes are 2 less than the zeroes of q(x).2025
• α and β are zeroes of a quadratic polynomial p x^2+q x+1. Form a quadratic polynomial whose zeroes are 2/(α) and 2/(β).2025
• Find the zeroes of the polynomial r(x)=4 x^2+3 x-1. Hence, write a polynomial whose zeroes are reciprocal of the zeroes of…2025
• If the sum of zeroes of the polynomial p(x)=2 x^2-k √2 x+1 is √2, then value of k is:2024
• If a polynomial p(x) is given by p(x)=x^2-5 x+6, then the value of p(1)+p(4) is:2024
• If α and β are zeroes of the polynomial 2 x^2-9 x+5, then value of α^2+β^2 is2024
• The zeroes of the quadratic polynomial 2 x^2-3 x-9 are:2024
• If α and β are zeroes of the polynomial 5 x^2+3 x-7, the value of 1/(α)+1/(β) is2024
• The zeroes of a polynomial x^2+p x+q are twice the zeroes of the polynomial 4 x^2-5 x-6. The value of p is:2024
• If α and β(α>β) are the zeroes of the polynomial -x^2+8 x+9, then (α-β) is equal to2024
• If the sum and the product of zeroes of a quadratic polynomial are 2 √3 and 3 respectively, then a quadratic polynomial is:2024
• What should be added from the polynomial x^2-5 x+4, so that 3 is the zero of the resulting polynomial?2024
• If α and β are the zeroes of the polynomial p(x)=kx^2-30 x+45 k and α+β=α β, then the value of k is:2024
• If α, β are the zeroes of the polynomial 6 x^2-5 x-4, then 1/(α)+1/(β) is equal to:2024
• A quadratic polynomial, one of whose zeroes is 2+√5 and the sum of whose zeroes is 4, is:2024
• What should be subtracted from the polynomial x^2-16 x+30, so that 15 is the zero of the resulting polynomial?2024
• Assertion: If the graph of a polynomial touches x -axis at only one point, then the polynomial cannot be a quadratic polynomial.…2024
• Assertion: Degree of a zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.2024
• If α and β are zeroes of the quadratic polynomial p(x)=x^2-5 x+4, then find the value of 1/(α)+1/(β)-2 α β.2024
• If α, β are zeroes of the polynomial p(x)=5 x^2-6 x+1, then find the value of α+β+α β.2024
• Find the zeroes of the quadratic polynomial x^2-15 and verify the relationship between the zeroes and the coefficients of the…2024
• Find the zeroes of the polynomial 4 x^2+4 x-3 and verify the relationship between zeroes and coefficients of the polynomial. OR…2024
• A ball is thrown in the air so that t seconds after it is thrown, its height h metre above its starting point is given by the…2024
• The graph of y=p(x) is given, for a polynomial p(x). The number of zeroes of p(x) from the graph is2023
• If one zero of the polynomial x^2-3 kx+4 k be twice the other, then the value of k is:2023
• The number of polynomials having zeroes -3 and 5 is:2023
• The zeroes of the polynomial 3 x^2+11 x-4 are:2023
• The number of quadratic polynomials having zeroes -5 and -3 is2023
• The sum of zeroes of the polynomial √2 x^2-17 are given as:2023
• If α, β are zeroes of a polynomial p(x)=2 x^2-x-1 then α^2+β^2 is equal to2023
• If α and β are the zeroes of the polynomial x^2-1, then the value of (α+β) is2023
• If α, β are the zeroes of a polynomial p(x)=x^2+x-1, then 1/(α)+1/(β) equals to2023
• If α, β are zeroes of the polynomial x^2-1, then value of (α+β) is:2023
• Which of the following is a quadratic polynomial with zeroes 5/3 and 0?2023
• The graph of y=p(x) is given in the adjoining figure. Zeroes of the polynomial p (x) are2023
• If one zero of the polynomial x^2+3 x+k is 2, then the value of k.2023
• If one zero of the polynomial 6 x^2+37 x-(k-2) is reciprocal of the other, then what is the value of k?2023
• If ' α ' and ' β ' are the zeroes of the polynomial ax^2-5 x+c and α+β=α β=10, then:2023
• The zeroes of the polynomial p(x)=x^2+4 x+3 are given by:2023
• Which of the following is a quadratic polynomial having zeroes -2/3 and 2/3?2023
• The number of polynomials having zeroes -1 and 2 is:2023
• If α and β are the zeroes of the quadratic polynomial p(x)=x^2-ax-b, then the value of α^2+β^2 is:2023
• If α, β are the zeroes of the polynomial p(x)=4 x^2-3 x-7, then (1/(α)+1/(β)) is equal to:2023
• If the zeroes of the quadratic polynomial x^2+(a+1) x+b are 2 and -3, then2023
• Assertion (A): The polynomial p(x)=x^2+3 x+3 has two real zeroes. Reason (R): A quadratic polynomial can have at most two real…2023
• If one zero of the polynomial p(x)=6 x^2+37 x-(k-2) is reciprocal of the other, then find the value of k.2023
• In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t…2023
• In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t…2023
• In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t…2023

Answers come from CBSE’s own marking schemes. How we source them.