Question

if 1 and -3 are roots of x3-ax2-13x+b find a and b

Answer 1

$\huge\mathfrak{Answer:}$

$p(x) = {x}^{3} - a {x}^{2} - 13x + b \\ p(1) = 0 \\ {1}^{3} - a ({1})^{2} - 13(1) + b = 0 \\ 1 - a - 13 + b = 0 \\ b - a = 12....(1) \\ p( - 3) = 0 \\ {( - 3)}^{3} - a( { - 3)}^{2} - 13( - 3) + b = 0 \\ - 27 - 9a + 39 + b = 0 \\ b - 9a = - 12....(2) \\ from(1) \: and \: (2) \\ a = 3 \\ b = 15$