If a - b -1- 6- q -0- b -0 then the roots of the equation ax 2- bx -5 a -0 is-areA- -1B- 1C- 5D- -5

The correct options are A 1 D 5 nbsp;a:b=1:6 ⇒ b=6a nbsp; ax^2+bx+5a=0 ⇒ a b+5a=0 We know that for a quadratic equation ax^2+bx+c=0, a,b,c∈ℝ if a b+c=0, ...

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Standard XII

Mathematics

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

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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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If a:b=1:6, a≠0, b≠0 then the roots of the equation ax2+bx+5a=0 is/are

The correct options are A −1 D −5 a:b=1:6 ⇒b=6a ax2+bx+5a=0 ⇒a−b+5a=0 We know that for a quadratic equation ax2+bx+c=0, a,b,c∈R if a−b+c=0, then roots are −1 and −ca Hence, roots of the required equation are −1 and −5.

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