Question

Determine the discriminant for the quadratic equation 0=-2x^2+3. Based on the discriminant value, how many real number solutions does this equation have ? Discriminant = b^2-4ac

Answer 1

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

Background of the Discriminant

The discriminant $b^2-4ac$ applies to quadratic equations when they are organised in standard form: $ax^2+bx+c=0$.

All quadratic equations can be solved with the quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$.

When $b^2-4ac$ is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

Solving the Problem

$0=-2x^2+3$

We are given above equation. Notice how there are values for a and c but none for b, as there is no bx term. This means that the value of b is 0. We can rewrite the equation so it shows this:

$0=-2x^2+0x+3$

Now that we have the values of a, b and c, we can plug them into the discriminant:

$D=0^2-4(-2)(3)\\D=-4(-2)(3)\\D=-4(-6)\\D=24$

Because 24 is positive, there are two real, distinct solutions for this equation.

I hope this helps!