Question 4: If (x - 2a) is a factor of 2x^{4} - 4ax^{3} + 7x^{2} - 13ax - 18, find the value of a.

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Let p(x) = 2x^{4} - 4ax^{3} + 7x^{2} - 13ax - 18

Because (x - 2a) is a factor of p(x), 2a is a zero of the polynomial.

∴ p(2a) = 0

p(2a) = 2(2a)^{4} - 4a(2a)^{3} + 7(2a)^{2} - 13a(2a) - 18 = 0

32a^{4} - 32a^{4} + 28a^{2} - 26a^{2} - 18 = 0

2a^{2} - 18 = 0

Or a^{2} = 9

Therefore, **a = ±3**

Class 9 Maths

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