Mathematics · 2021
JEE Main · 4 August 2021, Shift 2 · Q82
The integral value of a, for which the equation, (x^2+x+2)^2-(a-3)(x^2+x+2)(x^2+x+1)+(a-4)(x^2+x+1)^2=0 has real roots, is \ \ \ \.
The integral value of $\displaystyle a$, for which the equation,
$$\left(x^2+x+2\right)^2-(a-3)\left(x^2+x+2\right)\left(x^2+x+1\right)+(a-4)\left(x^2+x+1\right)^2=0
$$
has real roots, is \_\_\_\_.
Official answer
6
More from Quadratic Equations
- Let a, b ∈ R, a ≠ 0 be such that the equation, a x^2-2 b x+5=0 has a repeated root α, which is also a root of the equation, x^2-2 b x-10=0. If β is…2020
- Let a, b be two non-zero real numbers. If p and r are the roots of the equation x^2-8 a x+2 a=0 and q and s are the roots of the equation x^2+12 b…2022
- If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation (p^2+q^2) x^2-2 q(p+r) x+q^2+r^2=0 is also a root of the equation…2022
- Let a ∈ R and let α, β be the roots of the equation x^2+60^(1/4) x+a=0 If α^4+β^4=-30, then the product of all possible values of a is ____2023
- If α, β, where α<β, are the roots of the equation λ x^2-(λ+3) x+3=0 such that 1/(α)-1/(β)=1/3, then the sum of all possible values of λ is2026
- If the value of real number a>0 for which x^2-5 a x+1=0 and x^2-a x-5=0 have a common real root is 3/(√(2 β)) then β is equal to ____.2023
- Let S={x^3+a x^2+b x+c: a, b, c ∈ N. and.a, b, c ≤ 20} be a set of polynomials. Then the number of polynomials in S, which are divisible by x^2+2, is2026
- Let α, β be two roots of the equation x^2+(20)^(1/4) x+(5)^(1/2)=0. Then α^8+β^8 is equal to:2021
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.