determine the discriminant for the quadratic equation 0=-2x²+3. based on the discriminant value, how many…

determine the discriminant for the quadratic equation 0=-2x²+3. based on the discriminant value, how many real number solutions does the equation have? discriminant = b² - 4ac 0 1 2 24

determine the discriminant for the quadratic equation 0=-2x²+3. based on the discriminant value, how many real number solutions does the equation have? discriminant = b² - 4ac 0 1 2 24

Answer

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a quadratic equation is $ax^{2}+bx + c=0$. Rewrite $0=-2x^{2}+3$ as $-2x^{2}+0x + 3=0$. Here, $a=-2$, $b = 0$, and $c = 3$.

Step2: Calculate the discriminant

Use the formula $\text{Discriminant}=b^{2}-4ac$. Substitute $a=-2$, $b = 0$, and $c = 3$ into the formula: [ \begin{align*} b^{2}-4ac&=(0)^{2}-4\times(-2)\times3\ &=0 + 24\ &=24 \end{align*} ]

Step3: Determine the number of real - number solutions

If the discriminant $\Delta=b^{2}-4ac>0$, the quadratic equation has two distinct real - number solutions. Since $\Delta = 24>0$, the equation has 2 real - number solutions.

Answer:

Discriminant: 24, Number of real - number solutions: 2