Question

Show that 1/2 and -3/3 are the zeroes of the polynomial 4x^2+4x-3 and verify the relationship between zeroes and coefficients of polynomial .

Answer 1

Answer:

Step-by-step explanation:

4x^2+4x-3

Putting x=1/2

4*(1/2)^2+4*1/2-3

1+2-3

3-3

0

Therefore 1/2 is the zero of the polynomial

Putting x=-3/3=-1

4*(-1)^2+4*(-1)-3

4-4-3

-3

Therefore it's not the zero of the polynomial

Answer 2

Answer:

Given: 1/2 and -3/2 are the zeroes of the polynomial , p(x) = 4x² + 4x - 3

p(1/2) = 4(1/2)² + 4(1/2) - 3

         = 4(1/4)+ 2 - 3 = 1 - 1 = 0

p(-3/2) = 4 (-3/2)² + 4(-3/2) - 3

      =  9 - 6 - 3 = 0

So, 1/2 & -3/2 are zeroes of given polynomial

Sum of the zeroes = 1/2 + (-3/2) = 1/2 - 3/2 = -1

- coefficient of x / coefficient of x² = - 4 / 4 = -1

So,  Sum of the zeroes = - coefficient of x / coefficient of x²

Product of zeroes = 1/2 × -3/2 = - 3/4

constant term / coefficient of x² = -3 / 4

So, Product of zeroes = constant term / coefficient of x²

Hence Proved