Question

Find a quadratic polynomial whose zeros are the reciprocal of the zeros of 4 x square - 3 x minus 1

Answer 1

Given quadratic equation is-
4x2 - 3x - 1 = 0
We can find zeroes of this equation by splitting the middle term method.
4x2 - 3x - 1 = 0
4x2 - 4x + x - 1 = 0
4x(x-1) + 1(x-1) = 0
(4x+1) (x-1) = 0
4x+1=0 ; x-1=0
x= -1/4 ; x=1
*Zeroes of this quadratic equation are -1/4 & 1

According to question, zeroes of new quadratic equation are the reciprocal of zeroes of given quadratic equation, so the zeroes of new eqaution be a=-4 & b=1

sum of zeroes, a+b= -4+1
a+b= -3
product of zeroes, ab= -4×1
ab= -4

By the formula x2 - x(a+b) + ab=0, the required quadratic equation is-
x2 + 3x - 4 = 0.

Hope so u have understood the problem, and any confusion arrises, u may ask.

thanks......

Answer 2

hope it like you...