Question

for the following quadratic equation, find the discriminant. 2x² + 6x + 29 = 0

Explanation:

Step1: Recall discriminant formula

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

Step2: Identify coefficients

In the equation \(2x^2 + 6x + 29 = 0\), we have \(a = 2\), \(b = 6\), and \(c = 29\).

Step3: Substitute into formula

Substitute \(a = 2\), \(b = 6\), and \(c = 29\) into the discriminant formula:
\(D = (6)^2 - 4\times2\times29\)

Step4: Calculate each term

First, calculate \((6)^2 = 36\). Then, calculate \(4\times2\times29 = 232\).

Step5: Find the discriminant

Now, subtract: \(D = 36 - 232 = -196\).

Answer:

\(-196\)