Question

complex numbers online practice
complete this assessment to review what youve learned. it will not count toward your grade.

use the discriminant to determine the number of real solutions of $3x^2 = 16x + 12$. which of the following statements gives the correct explanation? (1 point)

• there will be two real solutions since the discriminant is positive.
• there will be one real solution since the discriminant is zero.
• there will be two real solutions since the discriminant is negative.
• there will be no real solutions since the discriminant is negative.

check answer remaining attempts: 3

Explanation:

Step1: Rewrite the equation in standard form

The standard form of a quadratic equation is \(ax^{2}+bx + c = 0\). Given \(3x^{2}=16x + 12\), we subtract \(16x\) and \(12\) from both sides to get \(3x^{2}-16x - 12=0\). Here, \(a = 3\), \(b=- 16\), and \(c=-12\).

Step2: Calculate the discriminant

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

$$
LATEXBLOCK0
$$

Step3: Analyze the discriminant

Since the discriminant \(D = 400>0\), for a quadratic equation, if the discriminant is positive, the equation has two distinct real solutions.

Answer:

There will be two real solutions since the discriminant is positive.