Question

If one root of the equation (k − 1)x2 − 10x + 3 = 0 is the reciprocal of the other, then the value of k is

Answer 1

Since in a equation of ax² + bx +c =0, the product of the roots is c/a, since we can assume the roots as y and 1/y, the value of k will come as 4

Answer 2

The value of k is 4

Step-by-step explanation:

Given:

one root of the equation $(k-1) x^2-10 x+3=0$ is  reciprocal of the other.

To find:

The value of k

Solution:

Consider that one root of equation is $\alpha$

So, other root is reciprocal of $\alpha$ which is $\frac{1}{\alpha}$

Now, we know that

Product of roots $=\frac{c}{a}$, where $c=3 \text { and } a=(k-1)$

Now applying the values of a and c, we get

$\alpha \times \frac{1}{\alpha}=\frac{3}{(k-1)}$

$1=\frac{3}{(k-1)}$

$k-1=3$

$k=3+1$

$k=4$

Therefore, the value of k is 4

To know more:

If one root of the quadratic equation kx²-3x-1=0 is 1/2 then find value of k

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