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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

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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.

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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
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.2 | Q 7 | Page 39
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