Question

what is the discriminant of the quadratic equation 3 - 4x = -6x²?
-68
-56
76
88

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a quadratic equation is \(ax^{2}+bx + c = 0\). Given the equation \(3-4x=-6x^{2}\), we add \(6x^{2}\) to both sides to get \(6x^{2}-4x + 3=0\). Here, \(a = 6\), \(b=-4\), and \(c = 3\).

Step2: Use the discriminant formula

The discriminant \(D\) of a quadratic equation \(ax^{2}+bx + c = 0\) is given by the formula \(D=b^{2}-4ac\). Substituting \(a = 6\), \(b=-4\), and \(c = 3\) into the formula, we get:

$$
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Answer:

-56 (corresponding to the option with -56, e.g., if the options are labeled as A. -68, B. -56, C. 76, D. 88, then the answer is B. -56)