Question

The polynomial p(x) = x4 - 2x3 + 3.x2 - ax + 3a - 7 when divided by x + 1 leaves the remainder 19.​

Answer 1

Answer:

a = 5

Step-by-step explanation:

We have been given that x⁴ - 2x³ + 3x² - ax + 3a - 7 when divided by divided by x + 1 gives remainder 19.

Subtract 19 from the equation:-

x⁴ - 2x³ + 3x² - ax + 3a - 26

This equation when divided by x+1 now gives remainder as zero.

Therefore, x + 1 is a zero of the equation.

So, x + 1 = 0

x = -1

Substitute the value of x:-

(-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 26 = 0

1 + 2 + 3 + a + 3a - 26 = 0

4a + 6 - 26 = 0

4a - 20 = 0

4a = 20

a = $\dfrac{20}{4}$

a = 5

So, the value of a is 5 !