Question

Find k if one zero of 4x square-2x+(k-4) is reciprocal of other

Answer 1

let the one zero be' a ' and its reciprocal zero be ' 1 / a '

Given quadratic equation :

4x^2 - 2x + ( k - 4 ) = 0. -----eq.(1)

since , we know quadratic equation is in the form :

ax^2 + bx + c = 0 ------------eq.(2)

on comparing eq.(1) and eq.(2) , we get

a = 4 , b = - 2 , c = k - 4

Find the product of zeroes :
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product of zeroes ( a, 1 / a ) = a × 1/a = 1

product of zeroes = c / a =( k - 4 )/ 4

solve for ' k ' :
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(k - 4 ) / 4 = 1

k - 4 = 4

k = 8

therefore, value of k = 8

Answer : k = 8

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