- Home
- Standard 12
- Mathematics
1.Relation and Function
hard
If $f(x)$ is a quadratic expression such that $f(1) + f (2)\, = 0$ , and $-1$ is a root of $f(x)\, = 0$, then the other root of $f(x)\, = 0$ is
A
$ - \frac{5}{8}$
B
$ - \frac{8}{5}$
C
$ \frac{5}{8}$
D
$ \frac{8}{5}$
(JEE MAIN-2018)
Solution
If $a$ and $-1$ are the roots of the polynomial, then we get
$f\left( x \right) = {x^2} + \left( {1 – a} \right)x – a$
$\therefore f\left( 1 \right) = 2 – 2a$
and $f\left( 2 \right) = 6 – 3a$
As, $f\left( 1 \right) + f\left( 2 \right) = 0$
$ \Rightarrow 2 – 2a + 6 – 3a = 0 \Rightarrow a = \frac{8}{5}$
Therefore, the other root is $\frac{8}{5}$
Standard 12
Mathematics
