i Find the quotient and remainder when x 4 x 3 3x 2 12x 6 is divided by (x 2 x 4) ii It is given that, when x 4 x 3 3 x2 px q is divided by (x 2 x 4), the remainder is zero Find the values of the constants p and q iii When p and q have these values, show that there is exactly one real value of x sa...

i To find the quotient and remainder when x4 x3 3x2 12x 6 is divided by x2 x 4 we can use polynomial ...

i. Find the quotient and remainder when x 4 + x 3 + 3x 2 + 12x

Question:

i. Find the quotient and remainder when x⁴+ x³ + 3x² + 12x + 6 is divided by (x² − x + 4).
ii. It is given that, when x⁴ + x³+ 3^x2 + px + q is divided by (x² − x + 4), the remainder is zero. Find the values of the constants p and q.
iii. When p and q have these values, show that there is exactly one real value of x satisfying the equation x⁴ + x³ + 3x² + px + q = 0 and state what that value is.