Question

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

Answer 1

Answer:

D) non-real roots

Step-by-step explanation:

In the quadratic equation $ax^2 + bx + c = 0, a \neq 0$ 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

Answer 2

$\frac{-b+- \sqrt{b^{2} -4ac } }{2a}$
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.