Question

Find the zeroes of the quadratic polynomials t² – 15 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let f(x) = t² – 15

Now, if we recall the identity

(a² – b²) = (a – b)(a + b)

Using this identity, we can write

t² – 15 = (t – √15) (x + √15)

So, the value of t²– 15 is zero when t = √15 or t = – √15

Therefore, the zeroes of t²– 15 are √15 and – √15.

Verification

Now,

So, the relationship between the zeroes and the coefficients is verified.