Question

Question 1 (iv)
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.
iv) $=\frac{-3}{2\sqrt{5}},-\frac{1}{2}$

Answer 1

iv) Given that, sum of zeroes $\left(S\right)=-\frac{3}{2\sqrt{5}}$
and product of zeroes $\left(P\right)=-\frac{1}{2}$
$\therefore$ Required quadratic expression,
$F\left(x\right)=x^2–Sx+P=x^2+\frac{3}{2\sqrt{5}}x-\frac{1}{2}$
$=2\sqrt{5}{x}^2+3x-\sqrt{5}$
Using factorization method = $2\sqrt{5}{x}^2+5x–2x–\sqrt{5}$
$=\sqrt{5}x(2x+\sqrt{5})-1(2x+\sqrt{5})$
$=(2x+\sqrt{5})(\sqrt{5}x-1)$
Hence, the zeroes of f(x) are $-\frac{\sqrt{5}}{2}and\frac{1}{\sqrt{5}}$