Question

find the find the GCD OF 2x2-18and x2-2x-3

Answer 1

Answer:

Let p(x)=x

2

+x−12 and q(x)=2x

2

−kx−9

Suppose, h(x)=(x−k) be HCF of p(x) and q(x)

Now, p(x)=x

2

+x−12

=x

2

+4x−3x−12

=x(x+4)−3(x+4)

=(x+4)(x−3)

So, either k=−4 or k=3. (i)

Since, (x−k) is HCF

∴q(x)=(x−k)g(x) for some factor g(x) of q(x)

Take x=k

⟹2(k)

2

−k×k−9=0

⟹2k

2

−k

2

−9=0

⟹k

2

=9⟹k=±3

From (i), we get

• k=3

Answer 2

Answer:

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