Question
Question: If x<sup>2</sup> –3x + 2 is a factor of x<sup>4</sup> + q – px<sup>2</sup> = 0 then p is...
If x2 –3x + 2 is a factor of x4 + q – px2 = 0 then p is
A
3
B
4
C
5
D
6
Answer
5
Explanation
Solution
As x2 –3x + 2 is factor of x4 – px2 + q = 0 so the roots of
x2 –3x + 2 = 0 will satisfy x4 – px2 + q = 0
So x2 –3x + 2 = 0
⇒ (x – 2) (x –1) = 0 ⇒ x = 1, 2
Putting x = 1, 1 – p + q = 0
⇒ p = 5
x = 2, 16 – 4p + q = 0