Use the discriminant to describe the roots of each equation. Then select the best description. 2 = x2 + 5x

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14-03-2018
Mathematics

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Use the discriminant to describe the roots of each equation. Then select the best description. 2 = x2 + 5x

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Professor1994 Professor1994 · Answer 1 · 2018-03-14T17:21:54+01:00

2=x^2+5x

We must write the equation in the form:
ax^2+bx+c=0
With all the terms in one side of the equation

2-2=x^2+5x-2
0=x^2+5x-2
x^+5x-2=0

Comparing with the general form of a quadratic equation:
Coefficient of x^2: a=1
Coefficient of x: b=5
Independent term: c=-2

Discriminant: D=b^2-4ac
D=5^2-4(1)(-2)
D=25+8
D=33

The discriminant is greater than zero (positive):
D=33>0 (+)

Then the equation has two different real roots