Question

Find the zeroes of the polynomial p(x) = 3x² + x – 10 and verify the relationship between the zeroes and its coefficients.

Answer 1

Given polynomial p(x) = 3x² + x – 10

⇒ 3x² + 6x – 5x – 10 = 0

⇒ 3x(x + 2) – 5(x + 2) = 0

⇒ (x + 2) (3x – 5) = 0

x + 2 = 0, 3x – 5 = 0

x = –2, x = `5/3`

Roots are α = –2, β = `5/3`

Here a = 3, b = 1, c = –10

Relationship between zeroes:

Sum of zeroes = `(-b)/a`

`α + β = (-b)/a`

`(-2)/1 + 5/3 = (-1)/3`

`(-6 + 5)/3 = (-1)/3`

`(-1)/3 = (-1)/3`

Product of zeroes = `c/a`

`αβ = c/a`

`-2 xx 5/3 = (-10)/3`

`(-10)/3 = (-10)/3`

Hence verified.