Question

Question 1 (ii)
Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials
(ii) $3x^2+4x–4$

Answer 1

(ii) $3x^2+4x–4$
Let $f\left(x\right)=3x^2+4x–4$
$=3x^2+6x–2x–4$ [by splitting the middle term]
=(x + 2) (3x – 2)
So, the value of $3x^2+4x–4$ is zero when $x+2=0$ or 3x – 2 = 0, i.e., when $x=-2orx=\frac{2}{3}$
so, the zeroes of $3x^2+4x–4are-2and\frac{2}{3}$
$\therefore$ Sum of zeroes = $-2+\frac{2}{3}=-\frac{4}{3}$
$=(-1)\left[\frac{Coefficientofx}{Coefficientof{x}^2}\right]$
And product of zeroes = $(-2)\left(\frac{2}{3}\right)=\frac{-4}{3}$
$=(-1{)}^2\left(\frac{Constantterm}{Coefficientof{x}^2}\right)$
Hence, verified the relations between the zeroes and the coefficients of the polynomial.