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Nature of Roots

If a : b =1: ...

Question

If $a : b = 1 : 6, a \neq 0, b \neq 0$ then the roots of the equation $a x^{2} + b x + 5 a = 0$ is/are

A

- 1

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B

1

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C

5

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D

- 5

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Solution

The correct options are
A $- 1$
D $- 5$
$a : b = 1 : 6$
$\Rightarrow b = 6 a$
$a x^{2} + b x + 5 a = 0$
$\Rightarrow a - b + 5 a = 0$

We know that for a quadratic equation $a x^{2} + b x + c = 0, a, b, c \in R$ if $a - b + c = 0,$ then roots are $- 1$ and $- \frac{c}{a}$
Hence, roots of the required equation are $- 1$ and $- 5.$

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Nature of Roots

Standard XII Mathematics

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