Question

Question 1 (i)
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
i) $\frac{-8}{3},\frac{4}{3}$

Answer 1

(i) given that, sum of zeroes (S) = $-\frac{8}{3}$
and product of zeroes (P) = $\frac{4}{3}$
$\therefore$ Required quadratic expression, $f\left(x\right)=x^2–Sx+P$
$=x^2+\frac{8}{3}x+\frac{4}{3}=3x^2+8x+4$
Using factorization method
$3x^2+6x+2x+4$
$=3x(x+2)+2(x+2)=(x+2)(3x+2)$
Hence, the zeroes of f(x) are – 2 and $-\frac{2}{3}$