If one root of the quadratic equation x²  + 5x + k=0 is 2, what is the value of k?
-10

12

-14

10

Given that one root of the quadratic equation \(x^2 + 5x + k = 0\) is 2, we can substitute this root into the equation to find the value of \(k\).

The quadratic equation is:

\[
x^2 + 5x + k = 0
\]

Substituting \(x = 2\) into the equation:

\[
(2)^2 + 5(2) + k = 0
\]

Simplifying this:

\[
4 + 10 + k = 0
\]

\[
14 + k = 0
\]

\[
k = -14
\]

So, the correct value of \(k\) is \(-14\).

Would you like more details or have any questions? Here are some related questions:

1. What is the formula to find the sum of the roots of a quadratic equation?
2. How do you determine the other root of the quadratic equation if one root is known?
3. What is the discriminant, and how does it relate to the roots of a quadratic equation?
4. How can you factorize a quadratic equation when you know its roots?
5. What is the general form of a quadratic equation?

**Tip:** When solving quadratic equations, always check if the quadratic can be factored easily or if using the quadratic formula would be more efficient.

Learn how to find the value of k in the quadratic equation x^2 + 5x + k = 0 when one root is given as 2. Step-by-step solution provided, covering algebraic concepts such as quadratic equations and the quadratic formula. Suitable for students in Grades 7-9.

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