 if 4 is a root of the quadratic equation x²+kx+17=0, find the value of k.

If 4 is a root of the quadratic equation \( x^2 + kx + 17 = 0 \), it means that substituting \( x = 4 \) into the equation should satisfy it. Therefore, we can set up the following equation:

\[ 4^2 + k \cdot 4 + 17 = 0 \]

Now, simplify and solve for \( k \):

\[ 16 + 4k + 17 = 0 \]
\[ 4k + 33 = 0 \]
\[ 4k = -33 \]
\[ k = -\frac{33}{4} \]

So, the value of \( k \) is \( -\frac{33}{4} \).

Would you like more details or have any other questions? Here are some more problems you might find interesting:

1. If the quadratic equation \( x^2 + kx + c = 0 \) has roots 3 and -2, find the value of \( k \) and \( c \).
2. Solve the quadratic equation \( 2x^2 - 3x + 1 = 0 \) by factoring.
3. Determine the nature of the roots of the quadratic equation \( 5x^2 + 2x + 1 = 0 \).
4. If the sum and product of the roots of a quadratic equation are 7 and 10 respectively, form the quadratic equation.
5. Find the vertex of the quadratic function \( y = 3x^2 - 12x + 9 \).

**Tip:** When solving quadratic equations, always check if the roots satisfy the original equation to confirm the solution is correct.

Discover how to find the value of k in a quadratic equation where 4 is a root. Follow a detailed step-by-step solution with the quadratic equation formula. Suitable for high school students studying algebra and quadratic equations.

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