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

Sum

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

#### Solution

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

x^2 + bx + c = 0  .....(i)

Put b = 0 in equation (i)

We get x^2 + 0 + c = 0

⇒ x^2 - 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.

Concept: Nature of Roots of a Quadratic Equation
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10