Question

If roots 4x2 - 2x + c = 0 are reciprocal of each other then the value of c is ?

Answer 1

SOLUTION

TO DETERMINE

The value of c for the roots are are reciprocal of each other

$\sf{4 {x}^{2} - 2x + c = 0 }$

EVALUATION

Here the given equation is

$\sf{4 {x}^{2} - 2x + c = 0 }$

Let the roots of the equation are

$\displaystyle \sf{ \alpha \: \: \: and \: \: \frac{1}{ \alpha } }$

So by the given condition

$\displaystyle \sf{ \alpha \times \: \frac{1}{ \alpha } = \frac{c}{4} }$

$\displaystyle \sf{ \implies \: 1 = \frac{c}{4} }$

$\displaystyle \sf{ \implies \: c = 4 }$

FINAL ANSWER

The required value of c = 4

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. find the equation that formed by squaring each root of the equation x²+3x-2=0

https://brainly.in/question/33064705

2. find the equation that formed by increasing each root of 2x²-3x-1=0by 1

https://brainly.in/question/33063519