Question

if alpha and beta are zeros of polynomial p x = 2 X square + bx + c find the value of Alpha square minus beta square​

Answer 1

SOLUTION ;

value is  b^2 - 2ac/a^2

QUESTION ;

if alpha and beta are zeros of polynomial p x = 2 X square + bx + c find the value of Alpha square minus beta square

                            We know that alpha + beta =  - b/a

                                                    (alpha)(beta)  = c/a

 And ,  (a + b)^2 = a^2 + 2ab + b^2      ..........equ (1)

Also ,  (a -b) ^2 = a^2 - 2ab + b^2 .........equ(2)

that implies ;  a^2 + b^2 =  (a -b)^2 + 2ab   ......equ(3)

 

substitute equ (3) in equ (1)

we get , (a+ b )^2 = (a-b)^2 + 2ab

   or,    (a-b)^2 = (a+b)^2 - 2ab

substitute alpha and beta in place of 'a' and 'b' .

(alpha - beta)^2 = (alpha + beta )^2 - 2(alpha )(beta)

                                           alpha + beta =  - b/a

                                            (alpha)(beta)  = c/a

polynomial =  2x^2 + bx + c

b = b

a = 2

c= c  

substitute (alpha - beta)^2 = (alpha + beta )^2 - 2(alpha )(beta)

 (alpha - beta)^2 = (-b/a)^2 - 2c/a    

= b^2/a^2 - 2c/a

or, b^2 - 2ac/a^2