Question

If one root of the quadratic equation \(2x^2 + px - 3 = 0\) is \(-3\), then the value of \(p\) will be:

• A. \(3\)
• B. \(5\)
• C. \(4\)
• D. \(6\)

Hint:

When a value \(r\) is a root of \(ax^2+bx+c=0\), substituting \(x=r\) gives an equation in the unknown parameter(s). Alternatively, you can use the factor theorem \(a(r)^2+b(r)+c=0\).

Answer 1

The Correct Option is B

Step 1: Use the fact that a root satisfies the equation.
If \(x=-3\) is a root, substitute \(x=-3\) into \(2x^2 + px - 3 = 0\):
\[ 2(-3)^2 + p(-3) - 3 = 0 \;\Rightarrow\; 18 - 3p - 3 = 0. \]
Step 2: Solve for \(p\).
\[ 15 - 3p = 0 \;\Rightarrow\; 3p = 15 \;\Rightarrow\; p = 5. \]
Step 3: Conclude.
Therefore, \(p=5\).