Question

Find the zeroes of the polynomial p(x) = 3x² + 7x – 20 and verify the relationship between its zeroes and the coefficients.

Answer 1

p(x) = 3x² + 7x – 20

⇒ p(x) = 3x² + 12x – 5x – 20

⇒ p(x) = 3x(x + 4) – 5(x + 4)

⇒ p(x) = (3x – 5)(x + 4)

Now for finding the zeroes, put p(x) = 0

∴ (3x – 5)(x + 4) = 0

`x = 5/3; x = -4`

Let, `α = 5/3; β = -4`

Now, `α + β = 5/3 + (-4)`

= `(5 - 12)/3`

⇒ `α + β = (-7)/3`

And sum of zeroes = `(-b)/a`

= `(-7)/3`

`α + β = (-b)/a`

= `(-7)/3`

And `αβ = 5/3 xx (-4)`

= `(-20)/3`

`αβ = c/a`

= `(-20)/3`

LHS = RHS

Hence, verifies.