Question

for which value of m does the graph of $y = 18x^2 + mx + 2$ have exactly one x - intercept?
0
9
12
16

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^{2}+bx + c = 0\), the discriminant is \(\Delta=b^{2}-4ac\). When \(\Delta = 0\), the quadratic has exactly one real root (one \(x\)-intercept for the graph of \(y = ax^{2}+bx + c\)). Here, \(a = 18\), \(b=m\), \(c = 2\). So we set \(\Delta=m^{2}-4\times18\times2=0\).

Step2: Solve for m

Simplify the equation: \(m^{2}-144 = 0\). Then \(m^{2}=144\), so \(m=\pm12\). Among the options (0, 9, 12, 16), 12 is a solution.

Answer:

12 (corresponding to the option with 12, e.g., if the options are A. 0, B. 9, C. 12, D. 16, then the answer is C. 12)