Question

X^4-2x^3+3x^2-ax+8 is divided by (x-2) it leavws a remainder 10. Find the value of a

Answer 1

SOLUTION

The given polynomial is p(x) x^4 -2x^3+3x^2 -ax+8.

Given,the polynomial p(x) when divided by (x-2) leaves remainder 10.

Therefore,

p(2)= 10( Remainder theorem)

$= > (2) {}^{4} - 2 {(2)}^{3} + 3(2) {}^{2} - a(2) + 8 = 10 \\ = > 16 - 16 + 12 - 2a + 8 = 10 \\ = > 20 - 2a = 10 \\ = > - 2a = 10 - 20 \\ = > - 2a = - 10 \\ = > 2a = 10 \\ = > a = \frac{10}{2} = 5$

The value of a= 5

hope it helps ☺️

Answer 2

Answer

x - 2 = 0

x = 2

x^4 - 2x^3 + 3x^2 - ax + 8 = 0

=> (2)^4 - 2(2)^3 + 3(2)^2 - 2a + 8 = 10

=> 16 - 16 + 12 - 2a + 8 = 10

=> 20 - 2a = 10

=> 10 = 2a

=> a = 5