Question

Which equation has roots -2 and 3? A. y=x2+x−6 B. y=x2−x−6 C. y=x2−5x−6 D. y=x2+5x−6

Answer 1

The answer is B.

Explanation:

You have make y equals to 0 and solve each and every equation one by one :

Option A,

`{x}^(2) + x - 6 = 0 \\ {x}^(2) + 3x - 2x - 6 = 0 \\ x(x + 3) - 2(x + 3) = 0 \\ (x - 2)(x + 3) = 0 \\ x = 2 \: or \: - 3`

Option B,

`{x}^(2) - x - 6 = 0 \\ {x}^(2) - 3x + 2x - 6 = 0 \\ x(x - 3) + 2(x - 3) = 0 \\ (x + 2)(x - 3) = 0 \\ x = - 2 \: or \: 3`

Option C,

`{x}^(2) - 5x - 6 = 0 \\ {x}^(2) + x - 6x - 6 = 0 \\ x(x + 1) - 6(x + 1) = 0 \\ (x - 6)(x + 1) = 0 \\ x = 6 \: or \: - 1`

Option D,

`{x}^(2) + 5x - 6 = 0 \\ {x}^(2) - x + 6x - 6 = 0 \\ x(x - 1) + 6(x - 1) = 0 \\ (x + 6)(x - 1) = 0 \\ x = - 6 \: or \: 1`