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