Use the discriminant to describe the roots of each equation. Then select the best description.

1. x^2 - 5x + 7 = 0

2. x^2 - 5x - 4 = 0

3. 16x^2 + 8x + 1 = 0

4. x^2 + 9x + 14 = 0

here are the options

a. double root

b. real and rational root

c. real and irrational root

d. imaginary root

1. discriminant = b^2 - 4ac = (-5) ^2 - (4 x 1 x 7) = 25 - 28 = - 3 [imaginary root]

2. discriminant = (-5) ^2 - (4 x 1 x - 4) = 25 - (-16) = 25 + 16 = 41 [real and irrational root]

3. discriminant = (8) ^2 - (4 x 16 x 1) = 64 - 64 = 0 [double root]

discriminant = b^2 - 4ac if the discriminant is positive, there are 2 real roots

if it is negative, then there are 2 imaginary roots

if it is 0, then there is one real root

The coefficient of x^2 is a, the coefficient of x is b and the constant is c. so if you substitute the a, b and c to the equation of the discriminant shown above, you should have your answer.