Question

If alpha and beta are the zeroes of the quadratic polynomial f(x) equals 2x²-5x+7.find a polynomial whose zeroes are 2alpha +3beta and 3alpha +2bets

Answer 1

$\alpha + \beta = \frac{ - b}{a} = \frac{5}{2} \\ \alpha \beta = \frac{c}{a} = \frac{7}{2}$
to calculate
$2 \alpha + 3 \beta \: \: and \: 3 \alpha + 2 \beta$
we individually have the value of
$\alpha \: and \: \beta$
for that factorise the polynomial.
there should be -7 in the polynomial,instead of +7,otherwise it would not be factorise.