Question

PLEASE PLEASE PLEASE HELP Find the value of the discriminant. Then describe the number and type of roots for the equation.

Answer 1

ANSWER

The discriminant is 384. Because the discriminant is greater than 0 and is not a perfect square, the two roots are real and irrational.

EXPLANATION

The given quadratic equation is:

$- 3 {x}^{2} - 18x + 5 = 0$

We compare this equation to:

$a {x}^{2} + bx + c = 0$

We have a=-3,b=-18, and c=5.

The discriminant of a quadratic equation is calculated using the formula:

$D=b^{2} - 4ac$

We plug in the values to obtain:

$D= {( - 18)}^{2} - 4( - 3)(5)$

$D= 324 + 60$

Simplify:

$D= 384$

The discriminant is greater than zero, hence there are two distinct real roots.

Since 384 is not a perfect square, the roots are irrational.