Question

if alpha and beta are the zeros of the polynomial p(x)= 2x^2-7x+3 then find the value of a^2-b^2

Answer 1

${ \alpha }^{2} - { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ = \frac{49}{4} - 3 \\ ( \alpha + \beta = \frac{7}{2} \: and \: \alpha \beta = \frac{3}{2} ) \\ \frac{37}{4}$