Question

if x-2 is a factor of x³ - 2 ax²+ax-1, then the value of a is​

Answer 1

Given that,

(x-2) is a factor of x³ - 2 ax²+ax-1

• then, (x+2) = 0
• x = -2

Let's substitute x in x³ - 2 ax²+ax-1 and if the value of x³ - 2 ax²+ax-1 must be also zero

${( - 2)}^{3} - 2 \times a \times { ( - 2)}^{2} + a \times - 2 - 1 = 0 \\ - 8 - 2 \times a \times 4 + ( - 2a) - 1 = 0 \\ - 8 - 8a - 2a- 1 = 0 \\ - 10a = 0 + 1 + 8 \\ a = - 9 \div 10$

Therefore, the value of a is -9/10.

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