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.

iii) $-2\sqrt{3},-9$

Answer 1

iii) Given that, sum of zeroes $\left(S\right)=-2\sqrt{3}$
and product of zeroes $\left(P\right)=-9$
$\therefore$ Required quadratic expression
$f\left(x\right)=x^2–Sx+P=x^2+2\sqrt{3}x–9$
$=x^2+3\sqrt{3}x-\sqrt{3}x-9$
$=x(x+3\sqrt{3})–\sqrt{3}(x+3\sqrt{3})$
$=(x+3\sqrt{3})(x-\sqrt{3})$
Hence, the zeroes of f(x) are - $3\sqrt{3}and\sqrt{3}$