Question

Find the zeroes of the quadratic polynomials r²s²x² + 6rstx + 9t² and verify the relationship between the zeroes and the coefficients.

Answer 1

Let f(x) = r²s²x² + 6rstx + 9t²

Now, if we recall the identity

(a + b)² = a² + b² + 2ab

Using this identity, we can write

r²s²x² + 6rstx + 9t² = (rsx + 3t)²

On putting f(x) = 0 , we get

(rsx + 3t)² = 0

Thus, the zeroes of the given polynomial r²s²x² + 6rstx + 9t² are -3t/rs and -3t/rs.

Verification

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