Question

Compute the zeroes of the polynomial 4x2 – 4x – 8 = 0. Also, establish a relationship between the zeroes and coefficients

Answer 1

Answer:

α = -1

β = 2

Explanation:

αβ = c/a = -8/4 = -2

α + β = -b/a = 4/4 = 1

Answer 2

Factorise the equation 4x2 – 4x – 8 = 0

4x2 – 4x – 8 = 0

4x2 – 2x – 2x + 1 = 0

2x(2x – 1) – 1(2x -1) = 0

(2x – 1) (2x – 1) = 0

So, the roots of 4x2 – 4x – 8 are (½ and ½)

Relation between the sum of zeroes and coefficients:

½ + ½ = 1 = -4/-4 i.e. (- coefficient of x/ coefficient of x2)

Relation between the product of zeroes and coefficients:

½ × ½ = ¼ i.e (constant/coefficient of x2)