Answer:
The value of discriminant is 384
There are two different real roots for the equation
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