Extra Questions For Class 9 Maths Polynomials | Q4

Question 4: If (x - 2a) is a factor of 2x⁴ - 4ax³ + 7x² - 13ax - 18, find the value of a.

Video Explanation

Explanatory Answer | Chapter 2 Extra Question 4

Let p(x) = 2x⁴ - 4ax³ + 7x² - 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
32a⁴ - 32a⁴ + 28a² - 26a² - 18 = 0
2a² - 18 = 0
Or a² = 9

Therefore, a = ±3