Question

α,β are roots of y²-2y-7=0 find, a²+β²

Answer 1

Hi ,

Here I am using p , q instead of alfa and beta.

Compare y² - 2y - 7 = 0 with ay²+by+c = 0 ,we

get

a = 1 , b = -2 , c = -7

i ) sum of the roots = -b/a

p + q = - ( -2 )/1 = 2 ----( 1 )

ii ) product of the roots = c/a

pq = -7/1 = -7 ---( 2 )

Now ,

p² + q² = ( p + q )² - 2pq

= 2² - 2 × ( -7 )

[ from ( 1 ) and ( 2 ) ]

= 4 + 14

= 18

Therefore ,

alfa² + beta² = 18

I hope this helps you.

: )