1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f ( x ) be a quadratic polynomial such that f (-1)+ f (2)=0 . If one of the roots of f ( x )=0 is 3, then its other root lies in :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $f ( x )$ be a quadratic polynomial such that $f (-1)+ f (2)=0 .$ If one of the roots of $f ( x )=0$ is $3,$ then its other root lies in :

JEE MainJEE Main 2020Relations and Functions

Solution:

$f(x)=a(x-3)(x-\alpha)$
$f(2)=a(\alpha-2)$
$f(-1)=4 a(1+\alpha)$
$f(-1)+f(2)=0 \Rightarrow a(\alpha-2+4+4 \alpha)=0$
$a \neq 0 \Rightarrow 5 \alpha=-2$
$\alpha=-\frac{2}{5}=-0.4$
$\alpha \in(-1,0)$