Question

If x + a is a factor of 3x^2+6ax+5x-8=0. find a. ​

Answer 1

Answer:

If x + a is a factor of p(x) = 3x^2 +6ax+5x-8

then p(-a) = 0

$p( - a) = 3( - a) {}^{2} + 6a( - a) + 5( - a) - 8 \\ \: \: \: \: \: \: \: \: \: \: \: \: 0= 3a {}^{2} - 6a {}^{2} - 5a - 8 \\ - 3a {}^{2} - 5a = 8 \\ - 3a {}^{2} = 8 - 5a \\ - (3a {}^{2} ) = - ( - 8 + 5a) \\ 3a {}^{2} = 5a - 8 \\ 3a {}^{2} - 5a + 8 = 0$