Let f(x) be a quadratic expression such that | vedclass

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

Question

(D) Let $f(x) = ax^2 + bx + c$.Given $f(0) + f(1) = 0$,we have $c + (a + b + c) = 0$,which implies $a + b + 2c = 0$ $(i)$.Given $f(-2) = 0$,we have $4

Vedclass · Accepted Answer

$f\left(\frac{3}{5}\right)=0$

Vedclass · Answer

(D) Let $f(x) = ax^2 + bx + c$.Given $f(0) + f(1) = 0$,we have $c + (a + b + c) = 0$,which implies $a + b + 2c = 0$ $(i)$.Given $f(-2) = 0$,we have $4a - 2b + c = 0$ (ii).From $(i)$,$b = -a - 2c$. Substituting into (ii):$4a - 2(-a - 2c) + c = 0$ $\Rightarrow 4a + 2a + 4c + c = 0$ $\Rightarrow 6a + 5c = 0$.Let $a = 5k$,then $c = -6k$.Substituting into $(i)$: $5k + b + 2(-6k) = 0$ $\Rightarrow 5k + b - 12k = 0$ $\Rightarrow b = 7k$.Thus,$f(x) = k(5x^2 + 7x - 6) = k(5x^2 + 10x - 3x - 6) = k(5x(x + 2) - 3(x + 2)) = k(5x - 3)(x + 2)$.The roots are $x = -2$ and $x = \frac{3}{5}$.Therefore,$f\left(\frac{3}{5}\right) = 0$.

Let $f(x)$ be a quadratic expression such that $f(0)+f(1)=0$. If $f(-2)=0$,then

Similar Questions

The set of all values of $k > -1$,for which the equation $(3x^2 + 4x + 3)^2 - (k + 1)(3x^2 + 4x + 3)(3x^2 + 4x + 2) + k(3x^2 + 4x + 2)^2 = 0$ has real roots is:

The roots of the equation $x^3-3x-2=0$ are

If the roots of the equation $(b - c)x^2 + (c - a)x + (a - b) = 0$ are equal,then $a, b, c$ are in which progression?

If $m$ and $M$ are respectively the smallest and greatest rational roots of the equation $6x^6-25x^5+31x^4-31x^2+25x-6=0$,then $M-m=$

Suppose $a, b, c$ are real numbers,and each of the equations $x^2+2ax+b^2=0$ and $x^2+2bx+c^2=0$ has two distinct real roots. Then,the equation $x^2+2cx+a^2=0$ has

Vedclass Test Series

Exam Paper Generator

Online Exam Module