Mathematics · 2014
JEE Main · 19 April 2014, Shift 1 · Q72
If non-zero real numbers b and c are such that min f(x)> max g(x), where f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2(x ∈ R ); then |c/b| lies in the…
If non-zero real numbers b and c are such that $\displaystyle \min f(x)>\max g(x)$, where
$$\begin{aligned}
& f(x)=x^2+2 b x+2 c^2 \text { and } \\
& g(x)=-x^2-2 c x+b^2(x \in \mathbf{R}) ;
\end{aligned}
$$
then $\displaystyle \left|\frac{\mathrm{c}}{\mathrm{b}}\right|$ lies in the interval :
Official answer
(4)
$\displaystyle (\sqrt{2}, \infty)$
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
- The number of integral values of m for which the equation (1+m^2) x^2-2(1+3 m) x+(1+8 m)=0 has no real root is:2019
- 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
JEE Main 2014 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.