Question

Which of the following quadratic equations has −1 as a root?

Options

• x² − 4x − 5 = 0

• −x² − 4x + 5 = 0

• x² + 3x + 4 = 0

• x² − 5x + 6 = 0

Answer 1

x² − 4x − 5 = 0

Explanation:

We know that if the root of a quadratic equation is −1, then the quadratic equation will be satisfied by −1.

1. Since (−1)² − 4(−1) − 5

= 1 + 4 − 5

= 0

Therefore, −1 is a root of x² − 4x − 5 = 0.

2. Since − (−1)² − 4(−1) + 5

= −1 + 4 + 5

= 8 ≠ 0

Therefore, −1 is not a root of −x² − 4x + 5 = 0.

3. Since (−1)² + 3(−1) + 4

= 1 − 3 + 4

= 2 ≠ 0

Therefore, −1 is not a root of x² + 3x + 4 = 0.

4. Since (−1)² − 5(−1) + 6

= 1 + 5 + 6

= 12 ≠ 0

Therefore, −1 is not a root of x² − 5x + 6 = 0.