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Nature of Roots

For the equat...

Question

For the equation $x^{2} + b x + c = 0,$ if $1 + b + c = 0$ for all $b, c \in R,$ then roots are

A

1

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B

b

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C

c

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D

\frac{1}{c}

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Solution

The correct option is C $c$
If $a x^{2} + b x + c = 0$ be a quadratic & $a + b + c = 0,$ then $x = 1$ is one solution & the other solution will be $\frac{c}{a}$

$x^{2} + b x + c = 0$ and $1 + b + c = 0$
$\Rightarrow x = 1 & x = c$ are two solutions

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Nature of Roots

Standard XIII Mathematics

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