The sum of the roots of a quadratic equation is 
\[0\].
We are given that the equation is 
\[16x^2 + bx + c = 0\].
Find the value of 
\[b\].

To solve for the value of \( b \) in the quadratic equation \( 16x^2 + bx + c = 0 \), we can use the property that relates the sum of the roots of a quadratic equation to its coefficients.

For a general quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum of the roots \( \alpha + \beta \) is given by:

\[
\alpha + \beta = -\frac{b}{a}
\]

In the given quadratic equation \( 16x^2 + bx + c = 0 \), the coefficient \( a = 16 \), and the sum of the roots \( \alpha + \beta \) is given as \( 0 \). Therefore, we have:

\[
\alpha + \beta = -\frac{b}{16} = 0
\]

Since the sum of the roots is 0, we can set the equation above equal to 0:

\[
-\frac{b}{16} = 0
\]

To solve for \( b \), multiply both sides by 16:

\[
b = 0
\]

Thus, the value of \( b \) is \( \boxed{0} \).

Do you want further details or have any questions?

Here are five related questions to explore further:
1. What is the product of the roots of the quadratic equation?
2. How does the value of \( c \) affect the roots if \( b = 0 \)?
3. Can you derive the roots explicitly for this quadratic equation when \( b = 0 \) and \( c \) is known?
4. How does the discriminant relate to the nature of the roots in this equation?
5. What happens to the roots if we change the coefficient \( 16 \) in the equation to another value?

**Tip:** Always check the discriminant to determine whether the roots of a quadratic equation are real, equal, or complex.

Learn how to find the value of b in the quadratic equation 16x^2 + bx + c = 0, given that the sum of its roots is 0. This problem covers key algebraic concepts, including Vieta's formulas, quadratic equations, and the relationship between coefficients and roots. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation