Question

two solutions for all quadratic equations quick check
use the discriminant to determine the number of real solutions of $4x^2 + 3x - 7 = 0$. which of the following statements gives the correct explanation? (1 point)

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

Explanation:

Step1: Recall discriminant formula

For quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\).

Step2: Identify coefficients

In \(4x^2 + 3x - 7 = 0\), \(a = 4\), \(b = 3\), \(c = -7\).

Step3: Calculate discriminant

\(D = 3^2 - 4\times4\times(-7) = 9 + 112 = 121\).

Step4: Analyze discriminant

Since \(D = 121>0\), quadratic has two real solutions.

Answer:

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