Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$x { }^{2} - 2x - 8$
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Answer 1

Given equation is x²−2x−8

It can also be written as ⇒x²−4x+2x−8

=x(x−4)+2(x−4)

=(x−4)(x+2)

The value of x²−2x−8 is zero

when x−4=0 or x+2=0.

i.e, when x=4 or x=−2.

∴ The zeroes of x²−2x−8 are 4 and −2.

sum of zeroes =4+(−2)=2

product of zeroes =−2×4=−8.

Relationship between the zeroes and the coefficients for the standard quadratic equationa x²+bx+c=0 is:

Sum of roots = − a/b

Product of roots = a/c

Sum of roots = − -2/1

=-2

and Product of roots = −8/1

=−8

The relationship between the zeroes and the coefficients is verified.