Question

if one root of 4xsquare - 2x + (k - 4) = 0 be the reciprocal of the other, then find the value of k.

Answer 1

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Answer 2

Given,

One root of equation 4x² -2x + (k-4) = 0 is the reciprocal of the other root.

To find,

The value of k

Solution,

If the quadratic equation is of the form  ax²+bx+c = 0, then the products of the roots are given by c/a.

In the quadratic equation 4x² -2x + (k-4) = 0,

a =  4,  b =  -2,  c =  (k-4).

Since one root of the equation is reciprocal of the other the product of the root will be 1 as both the roots would cancel each other.

Suppose if one root is α then another root must be 1/α.

⇒    α ×  1/α = 1.

⇒    c/a = 1

⇒   (k-4)/4 = 1

⇒    k - 4 = 4

⇒   k = 8

Hence, the value of k =4 such that one root of the equation 4x² -2x + (k-4) = 0 is reciprocal of the other.