Question

Find the value of a, if x = – 1 is a zero of the polynomial:

ax3 + x2 – 2x + 4a – 9.​

Answer 1

$\tt x = - 1 \\ \\ \sf \: a {x}^{3} + {x}^{2} - 2x + 4a - 9 \\ \\ \sf = a {( - 1)}^{3} + {( - 1)}^{2} - 2( - 1) + 4a - 9 \\ \\ \sf = - 1a + 1 + 2 + 4a - 9 \\ \\ \sf = - 1a + 3 + 4a - 9 \\ \\ \sf = 3a - 6 = 0 \\ \\ \sf = 3a = 6 \\ \\ \sf = a = \frac{ \cancel6}{ \cancel3} = \frac{2}{1} = 2 \\ \\ \sf \huge \pink{a = 2}$