Question

Find the value of k for which roots are reciprocal to each other 3x2-10x+k

Answer 1

The value of k is 3.

Step-by-step explanation:

The given quadratic equation is

3x^2-10x+k=03x

2

−10x+k=0

It is given that one root of this quadratic equation is reciprocal of the other.

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

α

1

.

We know that,

\text{Sum of roots}=\frac{-b}{a}Sum of roots=

a

−b

....(1)

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

a

c

....(2)

Using equation (2) we get

\alpha \times \frac{1}{\alpha}=\frac{k}{3}α×

α

1

=

3

k

1=\frac{k}{3}1=

3

k

Multiply both sides by 3.

3=k3=k

Therefore the value of k is 3.

Answer 2

The value of k is 3.

Step-by-step explanation:

Given : Quadratic equation $3x^2-10x+k$.

To find : The value of k for which roots are reciprocal to each other ?

Solution :

In quadratic equation $3x^2-10x+k$,  a=3, b-10 and c=k.

It is given that one root of this quadratic equation is reciprocal of the other.

Let the roots be $\alpha \text{ and } \frac{1}{\alpha}$.

We know that,

$\text{Sum of roots}=\frac{-b}{a}$                    ....(1)

$\text{Product of roots}=\frac{c}{a}$               ....(2)

Using equation (2) we get

$\alpha \times \frac{1}{\alpha}=\frac{k}{3}$

$1=\frac{k}{3}$

Multiply both sides by 3.

$3=k$

Therefore, the value of k is 3.

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