Question 49

If $$x^2 + ax + b$$, when divided by $$x + 3$$, leaves a remainder of -1 and $$x^2 + bx + a$$, when divided by $$x - 3$$, leaves a remainder of 39, then $$a + b=?$$

Solution

From remainder theorem,

If polynomial is f(x) divided by the binomial (x-a) the remainder obtained f(a).

So,

f(-3) = $$x^2 + ax + b$$

$$-3^2-3a+b=-1$$

$$9-3a+b=-1$$

$$-3a+b=-10$$ -------I

Again

f(3)=$$x^2 + bx + a$$

$$3^2+3b+a=39$$

$$9+3b+a=39$$

$$3b+a=30$$ -------II

Equating I and II by multiplying I with 3

we get b= 8 and a= 6

So, a+b = 8+6= 14.

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