Question

if x^2 - 3 x + 2 is a factor of x^4-ax^2+b, find a and b​

Answer 1

Answer:

You can divide it you can proceed like this and if you put remainder to 0 you will get your ans

Answer 2

Answer:

If x2 – 3x + 2 is a factor of x4 – ax2 + b, then the remainder must be zero. x2 – 3x + 2 = 0 => x2 – 2x – x + 2 = 0 => (x – 2)(x – 1) = 0 => x – 2 = 0 or x – 1 = 0 => x – 1 = 0 => x = 1 or x – 2 = 0 => x = 2 P(x) = x4 – ax2 + b Putting x = 1, Remainder = P(1) = (1)4 – a x (1)2 + b = 0 => 1 – a + b = 0 => a – b = 1 …(1) Putting x = 2, Remainder = P(2) = (2)4 – a x (2)2 + b = 0 => 16 – 4a + b = 0 => 4a – b = 16 …(2) Subtracting eq. (1) from eq. (2) we get Putting the value of a = 5 in equation (1) a – b = 1 5 – b = 1 – b = – 4 b = 4 a = 5, b = 4Read more on Sarthaks.com - https://www.sarthaks.com/858994/if-x-2-3x-2-is-a-factor-of-x-4-ax-2-b-find-a-and-b