Question

Q. When 3x^2 - ax +8 is divided by (x - 2) and
5x^2 + ax -17 is divided by
(x +3) the remainders are the same. Find a

please let me know the answer of this Q

# answers needed with explanation
#no spam​

Answer 1

Step-by-step explanation:

When

$p(x) = 3 {x}^{2} - ax + 8$

is divided by x-2

and

$g(x) = 5 {x}^{2} + ax - 17$

is divided by x+3,then both remainders are same.

Method1: Divide both polynomial,then equate both remainders and solve for a

Method 2: Apply remainder theorem and then equate both remainders and solve for a

I am applying here method 2.

Remainder Theorem:

put x=2

$p(2) = 3 {(2)}^{2} - a(2)+ 8 \\ \\ = 12 - 2a + 8 \\ \\ p(2)= 20 - 2a$

Put x=-3,in g(x)

$g( - 3) = 5 {( - 3)}^{2} + a( - 3) - 17 \\ \\ = 45 - 3a - 17 \\ \\ g( - 3) = 28 - 3a$

Now according to the question,both remainders are same

$p(2) = g( - 3) \\ \\ 20 - 2a = 28 - 3a \\ \\ - 2a + 3a = 28 - 20 \\ \\ a = 8$

Hope it helps you.