Question

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

x2 - 5x + 7 = 0

double root
real and rational roots
real and irrational roots
non-real roots

Answer 1

`\frac{-b+- \sqrt{b^(2) -4ac } }{2a}`
This is the solution of the equation, where a=1, b=-5, c=7

So the discriminant is :
b^2-4ac=25-4*7= -3
The square root of -3 is non-real, this both solutions are non-real.

Answer 2

D) non-real roots

Explanation:

In the quadratic equation
`ax^2 + bx + c = 0, a \\eq 0` and

we know that the discriminant d =
`b^2 - 4ac`.

if d <0, then the roots are non-real roots

if d = 0, then double roots.

if d >0, then the roots are real and rational/irrational.

We are given
`x^2 -5x + 7 = 0`

Here a = 1, b = -5 and c = 7.

Let's find the discriminant d =
`(-5)^2 - 4*1*7`

d = 25 - 28

d = -3

Which is less than zero.

d < 0, so the roots are non-real according the definition stated above.

The answer is D) non-real roots