Math, asked by Fatma8894, 1 year ago

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

Answers

Answered by ALTAF11
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}
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