2)Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients i) x^2−2x−8
Solution:
Given polynomial is:
x² − 2x − 8
Comparing with ax² + bx + c, we get:
a = 1, b = −2, c = −8
Factorising:
x² − 4x + 2x − 8 = 0
(x − 4)(x + 2) = 0
Therefore, the zeroes are:
x = 4 and x = −2
Verification:
Sum of zeroes = 4 + (−2) = 2 = −b/a
Product of zeroes = 4 × (−2) = −8 = c/a
Hence verified.