Question

find the zeroes of the polynomial 4x2-3x-1 and verify the relationship between the zeroes and the coefficients of the polynomial

Answer 1

  4x2 - 3x - 1

= 4x2 - 4x + x - 1

= 4x (x - 1) + (x - 1)

= (4x + 1)(x - 1)

4x + 1 = 0 or x - 1 = 0

x = -1/4  or  x = 1

Sum of zeroes = 1 - 1/4 = 3/4

Product of zeroes = 1(-1/4) = -1/4

Hence verified.

Answer 2

Given,

A quadratic equation 4x²-3x-1 = 0.

To Verify,

The relationship between the zeroes and the coefficients of the polynomial.

Solution,

The given equation is

4x²-3x-1 = 0

4x²-4x+x-1 = 0

4x(x-1)+1(x-1) = 0

(4x+1)(x-1) = 0

So, x₁ = 1, x₂ = -1/4

Now,

Sum of roots = -b/a = 3/4

Also, x₁+x₂ = 1-1/4 = 3/4

Product of zeroes = c/a = -1/4

Also, x₁*x₂ = 1(-1/4) = -1/4

Hence verified.