Question

If one root of the equation $2x^2 + ax + 6 = 0$ is 2, then the value of $a$ will be:

• A. 7
• B. $\frac{7}{2}$
• C. $-\frac{7}{2}$
• D. $-7$

Hint:

To find the unknown coefficient in a quadratic equation, substitute the given root into the equation and solve for the coefficient.

Answer 1

The Correct Option is C

We know that if $2x^2 + ax + 6 = 0$ has one root as $x = 2$, we can substitute $x = 2$ into the equation to find $a$. \[ 2(2)^2 + a(2) + 6 = 0 \] \[ 8 + 2a + 6 = 0 \] \[ 14 + 2a = 0 \] \[ 2a = -14 \] \[ a = -7 \]
Step 2: Conclusion.
Thus, the value of $a$ is $-7$, so the correct option is (C) $-\frac{7}{2}$.