Quadratic Equations

CBSE Class 10 Mathematics · every board question from this chapter, 2022–2026

• If the quadratic equation 9 x^2+8 k x+16=0 has real and equal roots, then the value of k is2026
• The roots of the quadratic equation (x-1)^2=16 are:2026
• The value of k for which the equation k x^2-6 x-4=0 has real and equal roots, is2026
• In the given figure, a circle is centred at (1, 2). The diameter of the circle is2026
• The roots of the quadratic equation 4 x^2-(a-1)^2=0 are:2026
• The value of p for which roots of the quadratic equation x^2-p x+6=0 are rational, is2026
• If the roots of the quadratic equation √3 x^2-kx+2 √3=0 are real and equal, then the value(s) of k is/are:2026
• If roots of the quadratic equation x^2-k √3 x+2=0 are real and equal, then value of k is2026
• The value of m for which the quadratic equation 3 x^2-7 x+m=0 has real and equal roots, is2026
• Verify that roots of the quadratic equation (p-q) x^2+(q-r) x+(r-p)=0 are equal when q+r=2 p.2026
• The value of ' a ' for which a x^2+x+a=0 has equal and positive roots is:2025
• Which of the following quadratic equations has real and equal roots?2025
• Which of the following equations is a quadratic equation?2025
• If x/12-3/x=0, then the values of x are:2025
• Which of the following quadratic equations has real and distinct roots?2025
• If x^2+b x+b=0 has two real and distinct roots, then the value of b can be2025
• Which of the following equations is a quadratic equation?2025
• Which of the following equations does not have a real root?2025
• Which of the following equation is a quadratic equation?2025
• The discriminant of the quadratic equation bx^2+ax+c=0; b ≠ 0 is given by:2025
• Find the value(s) of 'k' so that the quadratic equation 4 x^2+kx+1=0 has real and equal roots. OR If ' α ' and ' β ' are the…2025
• The sides of a right triangle are such that the longest side is 4 m more than the shortest side and the third side is 2 m less…2025
• The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the triangle. OR A…2025
• A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the lawn and…2025
• If the roots of equation a x^2+b x+c=0, a ≠ 0 are real and equal, then which of the following relation is true?2024
• If the discriminant of the quadratic equation 3 x^2-2 x+c=0 is 16, then the value of c is:2024
• The ratio of the sum and product of the roots of the quadratic equation 5 x^2-6 x+21=0 is:2024
• If the quadratic equation ax^2+bx+c=0 has real and equal roots, then the value of c is:2024
• If y=1 is one of the solutions of the quadratic equation py^2+py+3=0, then the value of p is:2024
• Find the value of 'k' for which the quadratic equation (k+1) x^2-2(3 k+1) x+(8 k+1)=0 has real and equal roots. OR A 2-digit…2024
• Find the value of 'k' for which the quadratic equation (k+1) x^2-6(k+1) x+3(k+9)=0, k ≠-1 has real and equal roots. OR The age of…2024
• If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, then the area of the rectangle is reduced…2024
• A train travels a distance of 90 km at a constant speed. Had the speed been 15 km/h more, it would have taken 30 minutes less for…2024
• A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit,…2024
• Essel World is one of India's largest amusement parks that offers a diverse range of thrilling rides, water attractions and…2024
• Which of the following quadratic equations has sum of its roots as 4?2023
• The roots of the equation x^2+3 x-10=0 are:2023
• A quadratic equation whose roots are (2+√3) and (2-√3) is:2023
• If x=0 · 3, is a root of the equation x^2-0 · 9 k=0, then k is equal to:2023
• The least positive value of k, for which the quadratic equation 2 x^2+k x-4=0 has rational roots, is2023
• If the quadratic equation a x^2+b x+c=0 has two real and equal roots, then 'c' is equal to2023
• A quadratic equation whose roots are (3-√2) and (3+√2) is:2023
• If ' p ' is a root of the quadratic equation x^2-(p+q) x+k=0, then the value of 'k' is2023
• Statement A (Assertion): If 5+√7 is a root of a quadratic equation with rational co-efficients, then its other root is 5-√7.…2023
• Find the sum and product of the roots of the quadratic equation 2 x^2-9 x+4=0. OR Find the discriminant of the quadratic equation…2023
• Find the value of 'p' for which one root of the quadratic equation px^2-14 x+8=0 is 6 times the other.2023
• A natural number, when increased by 12, equals 160 times its reciprocal. Find the number. OR If one root of the quadratic…2023
• The sum of two numbers is 15. If the sum of their reciprocals is 3/10, find the two numbers. OR If α and β are roots of the…2023
• Find the value of 'p' for which the quadratic equation px(x-2)+6=0 has two equal real roots.2023
• While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by…2023
• While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by…2023
• Solve the quadratic equation: x^2+2 √2 x-6=0 for x.2022
• Find the value of 'k' for which the quadratic equation 2 k x^2-40 x+25=0 has real and equal roots. OR Solve for x: 5/2…2022
• Solve the quadratic equation for x: x^2-2 a x-(4 b^2-a^2)=0 OR If the quadratic equation (1+a^2) x^2+2 a b x+(b^2-c^2)=0 has…2022
• Find the value of m for which the quadratic equation (m-1) x^2+2(m-1) x+1=0 has two real and equal roots. OR Solve the following…2022
• If the sum of the roots of the quadratic equation ky^2-11 y+(k-23)=0 is 13/21 more than the product of the roots, then find the…2022
• For what value of m, the quadratic equation m x^2-2(m-1) x+(m+2)=0 has two real and equal roots? OR The diagonal of a rectangular…2022
• Solve the quadratic equation: x^2-2 a x+(a^2-b^2)=0 for x.2022
• The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his…2022
• Find the value of 'p' for which the quadratic equation p(x-4)(x-2)+ (x-1)^2=0 has real and equal roots. OR Had Aarush scored 8…2022
• In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a…2022

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