Question

identify the real zeros for f(x) = 3x² + 2x + 4. a 1 and -1 b 0 and -1 c no solution d infinite solutions

Explanation:

Step1: Recall the quadratic formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). The discriminant is \(D = b^2-4ac\). If \(D<0\), there are no real solutions.

Step2: Identify coefficients

For \(f(x)=3x^2 + 2x + 4\), we have \(a = 3\), \(b = 2\), \(c = 4\).

Step3: Calculate the discriminant

\(D=(2)^2-4\times3\times4=4 - 48=- 44\).

Step4: Analyze the discriminant

Since \(D=-44<0\), the quadratic equation \(3x^2 + 2x + 4 = 0\) has no real roots. So the function \(f(x)\) has no real zeros.

Answer:

C. no solution