Find the value of the discriminant. then describe the number and type of roots for the equation -3x2-18x+5=0

The value of discriminant is 384

There are two different real roots for the equation

Step-by-step explanation:

* Lets explain what is the discriminant

- In the quadratic equation ax² + bx + c = 0, the roots of the

 equation has three cases:

1- Two different real roots

2- One real root or two equal real roots

3- No real roots means imaginary roots

- All of these cases depend on the value of a , b , c

∵ The rule of the finding the roots is  

   x = [-b ± √(b² - 4ac)]/2a

- The effective term is b² - 4ac to tell us what is the types of

 the roots

# If the value of b² - 4ac is positive means greater than 0

∴ There are two different real roots

# If the value of b² - 4ac = 0

∴ There are two equal real roots means one real root

# If the value of b² - 4ac is negative means smaller than 0

∴ There is no real roots but the roots will be imaginary roots

∴ We use the discriminant to describe the number and type of roots

* Now lets solve the problem

∵ -3x² - 18x + 5 = 0

∴ a = -3 , b = -18 , c = 5

∵ Δ = b² - 4ac ⇒ (Δ is the discriminant symbol)

∴ Δ = (-18)² - 4(-3)(5) = 324 - (-60) = 324 + 60 = 384

∴ The value of discriminant is 384

∵ The value of discriminant greater then 0

∴ There are two different real roots for the equation

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

y = i/2 xtnop + (3i/2 tnop+ 1)

step-by-step explanation:

the picture is the step by step explanation.