Question

If x+2 is a factor of x2+2ax2+ax-1 then the value of a is

Answer 1

Solution:

Given that, (x + 2) is a factor of x² + 2ax² + ax - 1

Therefore if we substitute x = -2, we should get the value of the equation to be zero, since its a factor.

Therefore substituting in the equation we get:

→ (-2)² + 2a (-2)² + a (-2) - 1 = 0

→ 4 + 2a (4) - 2a - 1 = 0

→ 3 + 8a - 2a = 0

→ 6a + 3 = 0

→ 6a = -3

→ a = -3/6

→ a = -1/2

Hence the value of 'a' is -1/2.

Answer 2

Step-by-step explanation:

$\bf \red{Sub \: x = -2} \\ </p><p></p><p> \\ \bf \: { - 2}^{2} + 2a { - 2}^{2} + a (-2) - 1 = 0 \bf</p><p> \\ \bf \: 4 + 2a (4) - 2a - 1 = 0</p><p> \\ \bf \: 3 + 8a - 2a = 0</p><p> \\ \bf \: 6a + 3 = 0</p><p> \\ \bf \: 6a = -3 \\ \\ \bf \: a = \frac{ - 3}{6} \\ \\ </p><p> \bf \: \red{a = \frac{ - 1}{2} }$