Answer:
The discriminate is 76
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 discriminate value (D)
- The discriminate D = b² – 4ac determined from the coefficients of
the equation ax² + bx + c = 0.
# If the value of D positive means greater than 0
∴ There are two different real roots
# If the value of D = 0
∴ There are two equal real roots means one real root
# If the value of D is negative means smaller than 0
∴ There is real roots but the roots will be imaginary roots
∴ We use the discriminant to describe the roots
* Lets solve the problem
∵ 3x² - 10x = -2
- Put it in the form of ax² + bx + c = 0
- Add 2 for both sides
∴ 3x² - 10x + 2 = 0
- Compare between this equation and the form up to find a , b , c
∵ 3x² - 10x + 2 = 0 and ax² + bx + c = 0
∴ a = 3 , b = -10 , c = 2
- Lets find the discriminate D
∵ D = b² - 4ac
∵ a = 3 , b = -10 , c = 2
∴ D = (-10)² - 4(3)(2)
∴ D = 100 - 24 = 76
* The discriminate is 76
