If the coefficients of x³ and x⁴ in the expansion of (1 − ax)⁶ are equal, what is a?

Correct answer: d −4/3

the coefficient of x³ is −20a³ and of x⁴ is 15a⁴; −20a³ = 15a⁴ ⇒ a = −4/3, so this is the value.

Why the other options are wrong

• a 4/3: a = 4/3 makes −20a³ negative and 15a⁴ positive, which are not equal. The right answer is −4/3.
• b 3/4: a = 3/4 gives −20a³ ≠ 15a⁴. The right answer is −4/3.
• c −3/4: a = −3/4 gives −20a³ ≠ 15a⁴. The right answer is −4/3.