Question

what is the discriminant of the quadratic equation 0 = 2x² + 3x − 5?
○ −37
○ −31
○ 43
○ 49

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^{2}+bx + c = 0\), the discriminant \(D\) is given by \(D=b^{2}-4ac\).

Step2: Identify \(a\), \(b\), \(c\)

From the equation \(2x^{2}+3x - 5=0\), we have \(a = 2\), \(b = 3\), \(c=- 5\).

Step3: Substitute values into formula

Substitute \(a = 2\), \(b = 3\), \(c=-5\) into \(D=b^{2}-4ac\):
\[

$$\begin{align*} D&=(3)^{2}-4\times(2)\times(-5)\\ &=9 + 40\\ &=49 \end{align*}$$

\]

Answer:

49