Question

1. If x2 – 3x+2is a factor of“x^4 – px^2? +9=0, then (p,q)=

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Answer 1

Answer:

Step-by-step explanation:

X² - 3x + 2 is a factor of x⁴ - px² + q .

If it is a factor then remember that the numbers where X² - 3x + 2 will become = 0 are the numbers that will make the other polynomials value 0 .

Now we can put certain values of x in X² - 3x + 2 and try to find out exactly where does this become 0 . We find out that it becomes 0 at 1 and 2 i.e. when we put 1 in place of x in X² - 3x + 2 we get 0. Same goes with 2.

Now how did I get those value? Easy . Just factorise X²- 3x + 2 .

X² - 3x + 2 =0

X² -2x-x+2=0

(x-2)(x-1)=0

Therefore, x = 2,1

Now put the values of x obtained from here in the next polynomial. We get -

1 - p + q =0 and

16 - 4p + q =0

Subtracting both the equations we get

3p -15 = 0

P= 5

Now put p= 5 in 1-p+q = 0

We get q = 4.