Question

Find the discriminant if 3x^2-10x=-2

Answer 1

$3x^2-10x=-2\\3x^2-10x+2=0\\\\\Delta=(-10)^2-4\cdot3\cdot2=100-24=76$

Answer 2

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