Question

Find the zeroes of the polynomial 2x² + 7x + 5 and verify the relationship between its zeroes and coefficients.

Answer 1

2x² + 7x + 5 = 0

2x² + 2x + 5x + 5 = 0

2x(x + 1) + 5(x + 1) = 0

(x + 1)(2x + 5) = 0

x + 1 = 0, 2x + 5 = 0

x = –1 or x = `-5/2`

Roots are α = –1

`β = -5/2`

Here a = 2, b = 7, c = 5

Sum of roots = `- b/a`

`α + β = (-b)/a`

`-1 + ((-5)/2) = (-7)/2`

`(-2 - 5)/2 = (-7)/2`

`(-7)/2 = (-7)/2`

Product of roots = `c/a`

`αβ = c/a`

`-1 xx (-5)/2 = 5/2`

`5/2 = 5/2`

Hence verified.