Question

Question 2.
(x² + 2x - 15 ) is a factor of x + ax + bx - 30. Find the values of 'a and bº
Question 3.​

Answer 1

Answer:

Solution :

Let p(x)=x3+ax2−bx−30

Given p(x) is exactly divisible by x2−2x−15,i.e, (x−5)(x+3)

⇒p(x) is divisible by (x+3)and(x−5)

∴p(−3)=0andp(5)=0

consider p(−3)=0

⇒(−3)3+a(−3)2−b(−3)−30=0

⇒−27+9a+3b−30=0

⇒9a+3b−57=0

⇒3a+b−19=0 (1)

Now , consider p(5)=0

That is , 53+a(5)2−b(5)−30=0

⇒125+25a−5b−30=0

⇒25a−5b+95=0

⇒5a−b+19=0 (2)

Adding Eqs . (1)and (2) , we get

8a=0

⇒a=0

Subsrtituting a in Eq . (1) . we get b = 19.

∴ The required values of a and b are 0 and 19 respectively.

⇒p(x)=x3+0(x2)−19x−30.

That is , p(x)=x3−19x−30.

Thus , the third factor is x+2.

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