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 :

Question

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)  - (5/8) (B)  - (8/5) (C)  (5/8) (D)  (8/5)

Tardigrade Admin · Accepted Answer

Given one root of f(x) is -1. Then, f(x)=a(x+1)(x-α), α is other root of quadratic equation. Sof(1)+f(2)=0 ⇒ 2 a(1-α)+3 a(2-α)=0 ⇒ 2-2 α+6-3 α=0 ⇒ α=8 / 5

Q. 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 :

$- \frac{5}{8}$

$- \frac{8}{5}$

$\frac{5}{8}$

$\frac{8}{5}$

Given one root of $f (x)$ is $- 1$ .
Then, $f (x) = a (x + 1) (x - α), α$ is other root of quadratic equation.
So $f (1) + f (2) = 0$
$\Rightarrow 2 a (1 - α) + 3 a (2 - α) = 0$
$\Rightarrow 2 - 2 α + 6 - 3 α = 0$
$\Rightarrow α = 8/5$

Q. 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 :

−85​

−58​

85​

58​