Question

find the value of k for which one of the root of the quadratic equation kx²-14x+8=0 is 6 times the other.​

Answer 1

Here, it is given that one of the roots is six times the other. Let us assume one of the roots as x. Therefore, the other root will be 6x. On further simplification, we obtain the value of k =3.

Answer 2

Answer:

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The equation is,

kx²-14x+8=0

Sum of the roots,

$\alpha + \beta = \frac{14}{k}$

Product of the roots,

$\alpha \beta = \frac{8}{k}$

According to the question,

$\alpha = 6 \beta$

By using this,

$\alpha + \beta = \frac{14}{k}$

$7 \beta = \frac{14}{k}$

$\beta = \frac{2}{k}$

Now,

$6 { \beta }^{2} = \frac{8}{k}$

$6( \frac{4}{ {k}^{2} } ) = \frac{8}{k}$

$k = 3$

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