Question

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

x^2-5x+7=0

A.) Double Root
B.) Real and Rational Roots
C.) Real and Irrational Roots
D.) Non-real Roots

Answer 1

the discriminant is the part under the sqrt in the quadratic formula
for ax²+bx+c, the discriminant is b²-4ac


if the discriminant is
less than 0, then there are non-real roots
equal to 0, then there is a double root
greater than 0, then there are 2 real roots (may be rational or irrational)

so

1x²-5x+7

b²-4ac=(-5)²-4(1)(7)=25-28=-3
less than 0 so it is non real roots

answer is D

Answer 2

In a equation in the form $ax^2+bx+c=0$, the discriminant is $\Delta=b^2-4ac$. In this question:

$\Delta=(-5)^2-4\cdot1\cdot7\iff \Delta=25-28\iff\Delta=-3$

If $\Delta<0$, there are no real roots. $Option~D$