Question

use the discriminant to determine the number of real solutions of $3x^2 + 6x - 42 = 0$. (1 point)
□ real solution(s)

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^2 + bx + c = 0\), the discriminant \(D = b^2 - 4ac\). Here, \(a = 3\), \(b = 6\), \(c = -42\).

Step2: Calculate discriminant

Substitute values: \(D = 6^2 - 4\times3\times(-42)\)
\(= 36 + 504\)
\(= 540\)

Step3: Analyze discriminant

Since \(D = 540 > 0\), a quadratic equation with a positive discriminant has two distinct real solutions.

Answer:

two