Question

If the polynomials ax³+3x²-13and2x³-5x+a,when divided by(x-2)leave the same reaminder,find the value of a​

Answer 1

g(x) = x - 2 = 0

=> x = 2

p(x) = ax³ + 3x² - 13

p(2) = a(2)³ + 3(2)² - 13

Remainder = 8a + 12 - 13

Remainder = 8a - 1

p(x) = 2x³ - 5x + a

p(2) = 2(2)³ - 5(2) + a

Remainder = 16 - 10 + a

Remainder = 6 + a

Both these remainders are equal. Thus:

8a - 1 = 6 + a

=> 7a = 7

=> a = 1

Answer 2

Step-by-step explanation:

x-2=0

x=2

ax³+3x²-13=2x³-5x+a

a(2)³+3(2)²-13=2(2)³-5x+a

a(8)+3(4)-13=2(8)-5(2)+a

8a+12-13=16-10+a

8a-1=6+a

8a-a=6+1

7a=7

a=7/7

this may help u