if 4x-1 is a factor of 12x^3+px^2+qx-1 then find p and q
Answers
Given : 4x-1 is a factor of 12x^3+px^2+qx-1
To find : p & q
Solution:
3x² + x(p + 3)/4 + 1
4x - 1 _| 12x³+px²+qx-1 |_
12x³ - 3x²
___________
( p + 3)x² +qx-1
(p + 3)x² - x(p + 3)/4
_______________
x(4q + p + 3)/4 - 1
4x - 1
=> (4q + p + 3)/4 = 4
=> 4q + p + 3 = 16
=> 4q + p = 13
another method
4x - 1 is factor => x = 1/4
12(1/4)³ + p(1/4)² + q(1/4) - 1 = 0
=> 3/16 + p/16 + q/4 - 1 = 0
=> 3 + p + 4q - 16 = 0
=> p + 4q = 13
There is additional information required to get value of p & q
Few possible values
q = 0 , p = 13
q = 1 , p = 9
q = 2 , p = 5
q = 3 , p = 1
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