Final answer:
To find the value of k, we can use the fact that one of the roots of the equation is 4. By substituting the known value and solving for k using the quadratic formula, we get k = ±4. option c is correct .
Step-by-step explanation:
To find the value of k, we can use the fact that one of the roots of the equation is 4. A quadratic equation of the form ax²+bx+c = 0 can be solved using the quadratic formula. Plugging in the known values, we have:
[(-k ± √(k² - 4(-12)))/2]
Since one of the roots is 4, we can substitute that value into the formula:
[(-k ± √(k² - 4(-12)))/2] = 4
Simplifying and solving for k, we get:
-k ± √(k² + 48) = 8
Squaring both sides:
k² + 48 = 64
Simplifying further:
k² = 16
Taking the square root of both sides:
k = ±4
Therefore, the value of k can be either 4 or -4.