If(x-3) is the HCF of x 3 - 2x2+px+6 and x2 - 5x +q and find 6p + 5q
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Step-by-step explanation:
Given
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
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