Question

For what value of c, roots of quadratic equation 4x² - 2x + (c - 4) = 0 are reciprocal of each other.

Answer 1

Given: roots are reciprocal to each other.
Let the one zero be α and other zero be 1/α .

Given quadratic equation is 4x² - 2x + (c - 4)= 0

On comparing with ax² + bx + c
a= 4 , b= 2 , c= c-4

Product of zeroes(α.1/α)= c/a
α.1/α = (c - 4) /4
1 =  (c - 4) /4
4 = c -4
4+4 = c
c = 8

Hence, the value of c = 8

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Answer 2

Hey!!!

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your answer-

The equation: 4x^2 -2x +(c-4) = 0 … (1)

is said to have two roots, one of which is a reciprocal of the other. Let us re-write the equation as

x^2 -(2/4)x +(c-4)/4 = 0

Let the roots be m and 1/m so that their product = 1, or

(c-4)/4 =1, or

c-4 = 4, or

C = 8. Ans.

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