Determine the discriminant for the quadratic equation 0=-2x^2+3 Based on the discriminant value, how many real number
solutions does the equation have?

This problem has two number solutions. The solutions are x = ±√ 1.500 = ± 1.22474.

Step-by step explanation:

Step 1 :

Equation at the end of step 1 :

0 - ((0 - 2x2) + 3) = 0

Step 2 :

Trying to factor as a Difference of Squares :

2.1 Factoring: 2x2-3

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step 2 :

2x2 - 3 = 0

Step 3 :

Solving a Single Variable Equation :

3.1 Solve : 2x2-3 = 0

Add 3 to both sides of the equation :

2x2 = 3

Divide both sides of the equation by 2:

x2 = 3/2 = 1.500

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 3/2

The equation has two real solutions

These solutions are x = ±√ 1.500 = ± 1.22474