Question

Alpha and beta are the roots of y square - 2y-7 is equal to 7 find Alpha square + beta square

Answer 1

y^2-2y-14=0...
Alpha +beta =-b/a
Alpha +beta = 2....
Squaring both side we get....
(Alpha + beta)^2 =4
Alpha square + beta square + 2alpha*beta =4


We know that
Alpha *beta=c/a
So alpha* beta = -14
Put value in eq 1

Alpha square + beta square +2(-14)= 4
Alpha square + beta square = 32

Answer 2

y2-2y-7=7
=y2-2y-7-7=0
=y2-2y-14=0
= a=1; b= -2 ; c= -14
= alpha+beta= -b/a
                    = -(-2)/1
                    = 2
= alpha * beta=c/a
                     = -14/1
                     = -14
[its some what like (a+b)2 formula]

(alpha + beta)2 = alpha2 + beta2 + 2alpha* beta
(alpha + beta)2 - 2 alpha * beta = alpha2 + beta 2
(2)2 - 2(-14)= alpha2 + beta 2('coz we have to find alpha2 + beta2 we keep it one side and substitute the values of alpha + beta and alphabeta on the other side)

 alpha 2+ beta2 =4+28
                          =32
therefore alpha2 + beta2 =32