Question

if one root of equation 4x^2 - 2x + K-4 = 0 is recipracal of other the value of K is

A -8
B 8
C -4
D 4​

Answer 1

Answer:

Option B

Step-by-step explanation:

Given:-

One root of equation 4x^2 - 2x + K-4 = 0 is recipracal of other root .

To find:-

Find the value of K ?

Solution:-

Given quardratic equation is 4x^2 -2x+K-4 = 0

On comparing this equation with the standard quadratic equation ax^2+bx+c = 0

Then we have,

a = 4

b= -2

c= K-4

Let the other root be α

Then the one of the roots = reciprocal of the other root

The one of the roots = 1/α

We know that

Sum of the roots = - b/a

α + (1/α) = - (-2)/4

α + (1/α) = 2/4

α + (1/α) = 1/2 ----------------(1)

Product of the roots = c/a

(α)(1/α) = (K-4)/4

=> α/α = (K-4)/4

=> 1 = (K-4)/4

=> 1×4 = K-4

=> 4+4 = K

=> 8 = K

=> K = 8

Therefore, K = 8

Answer:-

The value of k for the given problem is 8

Used formulae:-

• The standard quadratic equation ax^2+bx+c = 0
• Sum of the roots = - b/a
• Product of the roots = c/a