Mathematics · 2019
JEE Main · 9 April 2019, Shift 1 · Q63
Let p, q ∈ R. If 2-√ 3 is a root of the quadratic equation, x^2+ p x+ q =0, then:
Let $\displaystyle p, q \in \mathbf{R}$. If $\displaystyle 2-\sqrt{3}$ is a root of the quadratic equation, $\displaystyle x^2+\mathrm{p} x+\mathrm{q}=0$, then :
Official answer
(2)
$\displaystyle q^2-4 p-16=0$
(3)
$\displaystyle \mathrm{p}^2-4 \mathrm{q}-12=0$
(4)
$\displaystyle q^2+4 p+14=0$
NTA’s answer key accepts any one of these.
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 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.