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

If the roots of the equation $x^2 + a^2 = 8x + 6a$ are real,then

The number of all $2$-digit numbers $n$ such that $n$ is equal to the sum of the square of the digit in its tens place and the cube of the digit in its units place is

The sum of all the real roots of the equation $(e^{2x} - 4)(6e^{2x} - 5e^x + 1) = 0$ is

Let $f(x) = ax^{2} + bx + c$ be such that $f(1) = 3$,$f(-2) = \lambda$,and $f(3) = 4$. If $f(0) + f(1) + f(-2) + f(3) = 14$,then $\lambda$ is equal to...

If $a, b$ are real numbers and $\alpha$ is a real root of $x^2 + 6x + 12 + 3 \sin(a + b\alpha) = 0$,then the value of $\cos(a + b\alpha)$ for the least positive value of $a + b\alpha$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module