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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

Verified Answer :

apologiabiology

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

arthurpdc

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. \(Option~D\)

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