Question

if Alpha , beta are the quadratic polynomial 2x²-3x+1 then find the value of beta² + Alpha²​

Answer 1

Answer:

First finding the zeroes of the polynomial 2x²-3x+1

2x²-2x-x+1 = 0

2x(x - 1)-1(x - 1) = 0

x = (x - 1)(2x - 1)

x = 1, 1

2

alpha = 1

beta = 1

2

alpha²+beta²

1²+ (1/2)²

this is in the form of (a + b)² = a² +b² +2ab

(1+1/2)² = 1² + 1/2² + 2( 1×1/2 )

= 1 + 1/4 + 1

= 2 + 1/4

= 9

4

hence beta² + Alpha² = 9 .

4