Question

P (x) = x⁴ - 7x² + ax + 1 gives equal remainders when divided by x-3 and x+1. Find a.​

Answer 1

Answer:

According to statement

$p(3) = p( - 1) \\ {3}^{4} - 7 {(4)}^{2} + 3a + 1 = {( - 1)}^{4} - 7 {( - 1)}^{2} - a + 1 \\ 81 - 128 + 3a = 1 - 7 - a \\ - 47 + 3a = - 6 - a \\ 4a = 41 \\ a = \frac{41}{4}$