To find the value of [tex]\( p \)[/tex] in the quadratic equation [tex]\( x^2 + px - 4 = 0 \)[/tex], given that -4 is one of the roots, we can use the fact that if [tex]\(-4\)[/tex] is a root, then it must satisfy the equation. Here’s a step-by-step solution:
1. The quadratic equation is given by [tex]\( x^2 + px - 4 = 0 \)[/tex].
2. Substitute [tex]\( x = -4 \)[/tex] into the equation because [tex]\(-4\)[/tex] is a root:
[tex]\[
(-4)^2 + p(-4) - 4 = 0
\][/tex]
3. Simplify the equation:
[tex]\[
16 - 4p - 4 = 0
\][/tex]
4. Combine like terms:
[tex]\[
12 - 4p = 0
\][/tex]
5. Solve for [tex]\( p \)[/tex]:
[tex]\[
12 = 4p
\][/tex]
6. Divide both sides by 4:
[tex]\[
p = 3
\][/tex]
Thus, the value of [tex]\( p \)[/tex] is 3.
