Find the value of the discriminant. then describe the number and type of roots for the equation.

–3x2 – 18x + 5 = 0

the discriminant is 324. because the discriminant is greater than 0 and is a perfect square, the two roots are real and rational.

the discriminant is –384. because the discriminant is less than 0, the two roots are complex.

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

the discriminant is –264. because the discriminant is less than 0, the two roots are complex.

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:

We compare this equation to:

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

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

We plug in the values to obtain:

Simplify:

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

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

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.