Question

If b = 0, c < 0, is it true that the roots of x² + bx + c = 0 are numerically equal and opposite in sign? Justify.

Answer 1

Given that, b = 0 and c < 0 and quadratic equation,

x² + bx + c = 0  .....(i)

Put b = 0 in equation (i), we get

x² + 0 + c = 0

⇒ x² = – c   ......`[("Here"  c > 0),(therefore - c > 0)]`

∴ x = `+-  sqrt(-c)`

So, the roots of x² + bx + c = 0 are numerically equal and opposite in sign.