Question

findbthe zeroes of the polynomial t square -15 and verify the relationship between the zeros and the coefficients of the polynomial​

Answer 1

Given :

• The quadratic polynomial t² - 15

To find :

• The zeros of the polynomial and verify the relationship between the zeros and the coefficients.

Solution :

Given polynomial :

→ t² - 15

This can be represented as :

→ (t)² - (√5)²

This is of the form a² - b² and can be represented as :-

→ (t + √15) (t - √15)

Therefore the zeros of the polynomial are :-

Verification :

Let α and β be √15 and - √15 and a, b and c be the coefficients of the polynomial.

Therefore :-

→ α = √15

→ β = - √15

→ a = 1

→ b = 0

→ c = -15

→ α + β = √15 - √15 = 0 = 0/1 = -(b)/a

→ α × β = √15 × - √15 = -15 = -15/1 = c/a

Hence the relationship is verified.