If f(x) is a quadratic expression such that f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the quadratic expression be $f(x) = k(x - r_1)(x - r_2)$.Given that $-1$ is a root,let $r_1 = -1$. Let the other root be $a$.So,$f(x) = k(x +

Vedclass · Accepted Answer

$\frac{8}{5}$

Vedclass · Answer

(D) Let the quadratic expression be $f(x) = k(x - r_1)(x - r_2)$.Given that $-1$ is a root,let $r_1 = -1$. Let the other root be $a$.So,$f(x) = k(x + 1)(x - a) = k(x^2 + (1 - a)x - a)$.We are given $f(1) + f(2) = 0$.$f(1) = k(1 + 1)(1 - a) = 2k(1 - a) = 2k - 2ka$.$f(2) = k(2 + 1)(2 - a) = 3k(2 - a) = 6k - 3ka$.Summing these: $f(1) + f(2) = (2k - 2ka) + (6k - 3ka) = 8k - 5ka$.Setting the sum to zero: $8k - 5ka = 0$.Since $f(x)$ is a quadratic expression,$k 
eq 0$,so we can divide by $k$.$8 - 5a = 0 \Rightarrow 5a = 8 \Rightarrow a = \frac{8}{5}$.Thus,the other root is $\frac{8}{5}$.

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

Similar Questions

In the real number system,the equation $\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1$ has

The number of real roots of the equation $e^{4x} - e^{3x} - 4e^{2x} - e^{x} + 1 = 0$ is equal to $.....$

If the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign,then the product of the roots will be

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x^2-9x-36=0$ and $\alpha < \beta < \gamma$,then find the value of $\alpha+2\beta+3\gamma$.

$2+\sqrt{5}$ and $1$ are roots of the cubic equation given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module