Question

15. If x^2-3x+2 is a factor of x^4-ax^2+b then find the values of'a' and 'b'.​

Answer 1

Step-by-step explanation:

Given :-

x^2-3x+2 is a factor of x^4-ax^2+b

To find :-

Find the values of 'a' and 'b'.?

Solution :-

Given polynomial = P(x) = x^4-ax^2+b

Given factor of P(x) = x^2-3x+2

=> x^2-x-2x+2

=>x(x-1)-2(x-1)

=> (x-1)(x-2) is a factor of P(x)

We know that

By Factor Theorem,

If x-1 is a factor of P(x) then P(1) = 0

Since x-1 = 0 => x = 1

P(1) = (1)^4 -a(1)^2+b = 0

=> 1 - a(1) +b = 0

=> 1-a+b = 0

=> a = 1+b ------------(1)

If (x-2) is a factor of P(x) then P(2)= 0

Since , x-2 = 0 => x = 2

=> P(2) = (2)^4-a(2)^2+b = 0

=> 16-a(4)+b = 0

=> 16-4a + b = 0

=> 16-4(1+b) +b = 0

=> 16-4-4b +b = 0

=> 12-3b = 0

=> 3b = 12

=> b = 12/3

=> b = 4

Now,

On Substituting the value of b in (1)

=> a = 1+4 = 5

Therefore, a = 5 and b = 4

Answer:-

The values of a and b are 5 and 4 respectively.

Used formulae:-

Factor Theorem:-

Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P(x) then P(a) = 0 vice-versa.

Answer 2

Hello, Buddy!!

✰ Given:-

• x²-3x+2 is a factor of x⁴-ax²+b.

✰ To Find:;

• Value of a & b.

✫ Required Solution:-

$\pink{\bold{Refer\;The\; Attachment}}$ ⤴️

• Value of a ☞ 5
• Value of b ☞ 4

$\boxed{\tt{@MrMonarque}}$

Hope This Helps!!