Mathematics · 2023
JEE Main · 30 January 2023, Shift 2 · Q82
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 ____.
If the value of real number $\displaystyle a>0$ for which $\displaystyle x^2-5 a x+1=0$ and $\displaystyle x^2-a x-5=0$ have a common real root is $\displaystyle \frac{3}{\sqrt{2 \beta}}$ then $\displaystyle \beta$ is equal to $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
13
More from Quadratic Equations
- 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
- 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
- The number of integral values of k, for which one root of the equation 2 x^2-8 x+k=0 lies in the interval (1,2) and its other root lies in the…2023
- Let α, β be the roots of the equation x^2-x+p=0 and γ, δ be the roots the equation x^2-4 x+q=0; p, q ∈ Z. If α, β, γ, δ are in G.P., then |p+q|…2026
- The equation x^2-4 x+[x]+3=x[x], where [x] denotes the greatest integer function, has:2023
- Let a, b, c be the lengths of three sides of a triangle satistying the condition (a^2+b^2) x^2-2 b(a+c) x+(b^2+c^2)=0. If the set of all possible…2024
- Let the equation x(x+2)(12-k)=2 have equal roots. Then the distance of the point (k, k/2) from the line 3 x+4 y+5=0 is2025
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.