Question

31. If (x-3) is the HCF of x3- 2x2 + px + 6 and x2 -- 5x + 9, find 6p+5q

Answer 1

Step-by-step explanation:

If(x-3) is the HCF of x 3 - 2x2+px+6 and x2 - 5x +q and find 6p

If(x-3) is the HCF of x 3 - 2x^2 + px+6 and x2 - 5x +q and find 6p + 5q

Given equation will be  

So hcf is x – 3  

Now x – 3 is a factor of both the expressions

So x – 3 = 0

Or x = 3

Substitute the values of x in the given equations we get

So x^3 – 2 x^2 + px + 6  

Put x = 3 we get

3^3 – 2(3)^2 + 3p + 6 = 0

9 – 18 + 3p + 6 = 0

15 – 18 + 3p = 0

3p = 3

Or p = 1  

Also x^2 – 5x + q = 0

      3^2 – 5(3) + q = 0

      9 – 15 + q = 0

   So q = 6

Now 6p + 5q will be 6(1) + 5(6)

                                  6 + 30

                                    36