Question

Match each quadratic equation with its roots.

1)a^2 - 2a + 10 = 0
2)a^2 - a + 12 = 0
3)2^2 - 2a + 15 = 0
4)a^2 - a + 11 = 0
Options for roots:
a = 1 + 5i
a = 1 - 7i
a = 1 + i/43

Answer 1

The roots of each quadratic equation are as follows: a² - 2a + 10 = 0 has complex roots, a = 1 + 5i and a = 1 - 5i. a² - a + 12 = 0 has real roots, a = 3 and a = 4. 2^2 - 2a + 15 = 0 has imaginary roots, a = 1 + i/4 and a = 1 - i/4. a² - a + 11 = 0 has real roots, a = 5 and a = 6.

Step-by-step explanation:

To find the roots of a quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

1. For the equation a² - 2a + 10 = 0, the roots are complex: a = 1 + 5i and a = 1 - 5i.
2. For the equation a² - a + 12 = 0, the roots are real: a = 3 and a = 4.
3. For the equation 2^2 - 2a + 15 = 0, the roots are imaginary: a = 1 + i/4 and a = 1 - i/4.
4. For the equation a² - a + 11 = 0, the roots are real: a = 5 and a = 6.