Question

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

Answer 1

Real and irrational root

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* 1* -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.