Find the zeroes of the polynomial y2 + 3/2√5y – 5., and verify th

1.	Find the zeroes of the polynomial y2 + 3/2√5y – 5., and verify the relation between the coefficients and the zeroes of the polynomial.
Answer» By splitting the middle term y² + 3√5/2y - 5 = 0 2y² + 3√5y - 10 = 0 2y² + (4√5y - √5y) - 10 = 0 2y² + (4√5y - √5y) - 10 = 0 2y(y + 2√5) - √5(y + 2√5) = 0 (y + 2√5)(2y - √5) = 0 ⇒ y = - 2√5, √5/2 Verification: Sum of the zeroes = - (coefficient of x) ÷ coefficient of x² α + β = - b/a (- 2√5) + (√5/2) = - (3√5)/2 = - 3√5/2 = - 3√5/2 Product of the zeroes = constant term ÷ coefficient of x² α β = c/a (- 2√5)(√5/2) = - 5 - 5 = - 5

Find the zeroes of the polynomial y2 + 3/2√5y – 5., and verify the relation between the coefficients and the zeroes of the polynomial.

Answer»

By splitting the middle term

y² + 3√5/2y - 5 = 0

2y² + 3√5y - 10 = 0

2y² + (4√5y - √5y) - 10 = 0

2y(y + 2√5) - √5(y + 2√5) = 0

(y + 2√5)(2y - √5) = 0

⇒ y = - 2√5, √5/2

Verification:

Sum of the zeroes = - (coefficient of x) ÷ coefficient of x²

α + β = - b/a

(- 2√5) + (√5/2) = - (3√5)/2

= - 3√5/2 = - 3√5/2

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

(- 2√5)(√5/2) = - 5

- 5 = - 5