Question

Find the zeroes of the quadratic polynomial x² + 6x + 8 and verify the relationship between the zeroes and the coefficients.

Answer 1

Given that,

Quadratic polynomial is x² + 6x + 8

`\implies` x² + 6x + 8

`\implies` x² + 4x + 2x + 8

`\implies` x(x + 4) + 2(x + 4)

`\implies` (x + 2)(x + 4)

Zeroes are – 2, – 4

Now, Sum of zeroes = – 2 + (– 4) = – 6

Product of zeroes = (– 2) × (– 4) = 8

Also, Sum of zeroes = `(-b)/a = (-6)/1` = – 6

Product of zeroes = `c/a = 8/1` = 8

Hence, relationship between zeroes and coefficients verified.