Question

find the value of k if the roots of equation (k²+2)x²+7x+3k=0 are the resiprocals of each other.​

Answer 1

Here is your answer:

Given that.

1) An expression kx² + 3x + 5.

2) The roots are reciprocal of each other.

To find,

The value of k.

Solution:

Let the roots be : \alpha \ and \ \frac{1}{ \alpha }α and

α

1

Then, We know that,

Product\ of\ roots = \frac{c}{a}Product of roots=

a

c

Here c = 5 & a = k

Then,

⇒ \alpha \times \frac{1}{ \alpha } = \frac{5}{k}α×

α

1

=

k

5

⇒ 1 = \frac{5}{k}1=

k

5

⇒ k = 5.k=5.

Therefore the value of k is 5.

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Hope my answer is helpful to you.