Question

PLEASEPLEASE help me how to solve this question when we substitute $5x^4-2x^3+7x^2-2x+1$ where $x=\frac{1-3i}{5}$

Answer 1

Answer:

1 is the answer for the given problem

Answer 2

Before we substitute, let's use remainder theorem.

$P(\alpha )$ is given when we divide by x-α.

If we found the remainder then it is the value $P(\alpha )$.

The divisor needs to be $x-\frac{1-3i}{5}$.

Multiply by 5. It will give the same remainder.

→$5x-1+3i$

Multiply by $5x-1+3i$. It still gives the remainder.

→$(5x-1)^2+9=25x^2-10x+10$

Divide by 5.

→$5x^2-2x+2$

Now let's use the division algorithm.

→$(5x^4-2x^3+7x^2-2x+1)\div (5x^2-2x+2)$

Quotient x²+1, Remainder -1

Therefore, the value is -1.