Question

show that 1/2 and -3/2 are the zeroes of the polynomial 4x square + 4x - 3 and also verify the relationship between the zeros and coefficients of the polynomial

Answer 1

Hii friend,

P(X) = 4X²+4X-3

=> 4X²+6X-2X-3

=> 2X(2X+3) -1(2X+3)

=> (2X+3)(2X-1)

=> (2X+3) = 0 OR (2X-1) = 0

=> X = -3/2 OR X = 1/2

Hence,

1/2 and -3/2 are the zero of the polynomial 4X²+4X-3

Let Alpha = 1/2 and Beta = -3/2

Relationship between the zeros and Coefficient.

Sum of zeros = (Alpha +Beta) = {1/2+(-3/2)} = 1/2 - 3/2 = 1-3/2 = -2/2 = -1 = Coefficient of X/Coefficient of X²

Product of zeros = (Alpha × Beta) = (1/2 × -3/2) = -3/4= Constant term/Coefficient of X².


HOPE IT WILL HELP YOU..... :-)

Answer 2

Hope U understand

Alpha is 1/2 and Beta is -3/2.

The product is -3/4

The sum is -1.