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Q.

Find the value of μ for which one root of the quadratic equation μx2−14x+8 = 0 is 6 times the other.

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a

5

b

4

c

3

d

2

answer is C.

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Detailed Solution

Given: The quadratic equation is μx2−14x+8 = 0
One root of the equation given is 6 times the other.
We need to find the value of μ
Let the roots of the given quadratic equation be α and β respectively.
According to the question,
α is 6 times of β
⇒α=6×β
Sum of the roots of the equation in general form ax2+bx+c=0 is

- \frac{b}{a}

Comparing the given equation μx2−14x+8 = 0 with the general form, we get
a=μ
b=−14
c=8
α+β

= - \frac{b}{a}

=

- (- \frac{14}{μ})

\Rightarrow α + β = \frac{14}{μ} \dots \dots . . Equation (1)

Given that α=6×β
Substituting α=6×β in Equation (1)
We get,

6 β + β = \frac{14}{μ}

\Rightarrow 7 β = \frac{14}{μ}

\Rightarrow β = \frac{2}{μ} \dots \dots . . Equation (2)

Product of the roots of the equation in general form ax2+bx+c=0 is ca

α \times β = \frac{c}{a} = \frac{8}{μ} \dots \dots . . Equation (3)

Substituting α=6×β in Equation (3)
We get,

6 β \times β = \frac{8}{μ}

\Rightarrow 6 β 2 = \frac{8}{μ} \dots \dots . . Equation (4)

Substituting Equation (2) in Equation (4) , we get

6 \times {(\frac{2}{μ})}^{2} = \frac{8}{μ}

\Rightarrow 6 \times \frac{4}{μ^{2}} = \frac{8}{μ}

\Rightarrow μ = 3

Therefore, the value of μ is 3.

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