Question

A polynomial $a{x}^3+b{x}^2$ + cx + d intersects the x - axis at 1 and -1, and y - axis at 2. The value of b is:

• A. -2
• B. 1
• C. 2

Answer 1

The correct option is A -2

We are given that the expression $a{x}^3+b{x}^2+cx+d$ intersects the x - axis at 1 & -1. It means that at x = 1 and -1 the value of the given polynomial is equal to 0.
$\therefore$ a + b + c + d = 0 & -a + b - c + d = 0
$\therefore$ 2(b + d) = 0
$\therefore$ b + d = 0 (1)
We are also given that, $a{x}^3+b{x}^2$ + cx + d intersects the y - axis at 2. This means that at x = 0, the value of the given polynomial is equal to 2.
0 + d = 2
$\therefore$ d = 2 (2)
From equations (1) & (2), b = -2