Answered

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


x2 - 5x - 4 = 0


double root

real and rational root

real and irrational root

imaginary root

Verified Answer :

Answer:

Real and irrational root

Step-by-step explanation:

Since a quadratic equation \(ax^2+bx+c\),

Has two real different roots,

If the value of discriminant \(D=b^2-4ac>0\)

Has two equal real roots,

If \(D=0\)

Has two imaginary roots,

If \(D<0\)

Here, the given equation,

\(x^2-5x-4=0\)

\(D=(-5)^2-4\times 1\times -4=25+16= 41>0\)

Hence, the equation has the two unequal real roots,

Now, √D is an irrational number ( Which can not be expressed in the form of p/q in which q≠0 )

Therefore, the given equation has real and irrational root,

Third option is correct.

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