Question 51

If $$x^2 + ax + b$$, when divided by $$x - 3$$, leaves a remainder of 22 and $$x^2 + bx + a$$, when divided by $$x - 3$$, leaves a remainder of 24, then $$a + b = ?$$

Solution

The correct option is C.

let p($$x$$)= $$x^{2}+ax+b$$ And f($$x$$) = $$x^{2}+bx+a$$

Now, p(3)= 22

$$\implies$$ $$3^{2}+3a+b$$ = 22

$$\implies$$ 3a+b = 13 ....... (1)

and, f(3) = 24

$$\implies$$ $$3^{2}+3a+b$$ = 24

$$\implies$$ 3a+b =15 ......(2)

Adding (1) and (2) we get, a+b = 7

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