Question

Question 1 (ii)
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.
ii) $\frac{21}{8},\frac{5}{16}$

Answer 1

ii) Given that, sum of zeroes $\left(S\right)=\frac{21}{8}$
and product of zeroes $\left(P\right)=\frac{5}{16}$
$\therefore$ Required quadratic expression, $f\left(x\right)=x^2–Sx+P$
$=x^2–\frac{21}{8}x+\frac{5}{16}=16x^2-42x+5$
Using factorization method = $16x^2–40x–2x+5$
$=8x(2x–5)–1(2x–5)=(2x–5)(8x–1)$
Hence, the zeroes of f(x) are $\frac{5}{2}and\frac{1}{8}$