Question

x2+ax+b when divided by x+3 leaves a remainder of 22 and x2+bx+a when divided by x-3 leaves a remainder of 24 then a+b is?

Answer 1

Answer:

The value of a+b = - 2.4 + 5.8 = 3.4

Step-by-step explanation:

first dividing $x^2 +ax+b$ by $x+3$ using long division method we get remainder as $b-(3a-9)$ (see Figure 1)

also given dividing $x^2 +ax+b$ by $x+3$ we get remainder as 22

Then , $b-(3a-9)=22$

Solving further,

$b-3a+9=22$

$b-3a=22-9$

$b-3a=13$ ................(1)

Again dividing $x^2 +bx+a$ by $x-3$ using long division method we get remainder as $a+3b+9$  (see Figure 2)

also given dividing $x^2 +bx+a$ by $x-3$ we get remainder as 24

Then , $a+3b+9=24$

$a+3b=24-9$

$a+3b=15$  .......(2)

Solving (1) and (2),  

Multiply equation (2) by 3

$3a+9b=45$  ..........(3)

Adding equation (1) and (3), We get,

$3a+9b+b-3a=13+45$

$9b+b=13+45$

$10b=58$

$b=5.8$

Put value of $b=5.8$ in (1) to solve for a, We get,

$5.8-3a=13$

$-3a=13-5.8$

$-3a=7.2$

$a=-2.4$  

Thus, the value of a+b = - 2.4 + 5.8 = 3.4.

Answer 2

Answer:

hii

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