Question

If alpha and beta are the roots of equation x^2+px+q=0 then what is alpha square+beta square

Answer 1

Hi Mate !!


Here's the Solution :-


Given equation :- x² + px + q = 0

Solution :-

• Sum of the Zeros =

$= \frac{ - coefficient \: of \: x}{coefficien \: of \: {x}^{2} }$

$\alpha + \beta = \frac{ - p}{1}$

• Product of Zeros

$= \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

$\alpha \beta = \frac{q}{1}$


Using identity :-

${( \alpha + \beta ) }^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta$

${( - p)}^{2} = { \alpha }^{2} + { \beta }^{2} + 2 \times \: q$

${p}^{2} - 2q = { \alpha }^{2} + { \beta }^{2}$