Math Problem Statement

Which equation has roots of -7 and 4?

Solution

To find the equation that has roots of 7-7 and 44, we need to remember that for a quadratic equation, the factors are based on the roots as follows:

If the roots are r1r_1 and r2r_2, the equation can be written as: (xr1)(xr2)=0(x - r_1)(x - r_2) = 0

Given the roots 7-7 and 44:

  1. Substitute r1=7r_1 = -7 and r2=4r_2 = 4.
  2. This gives us the factors (x+7)(x + 7) and (x4)(x - 4).
  3. So, the equation should be: (x+7)(x4)=0(x + 7)(x - 4) = 0

Answer: The correct option is A: (x+7)(x4)=0(x + 7)(x - 4) = 0.

Would you like further details or have any questions?

Here are some related questions:

  1. How do you find the roots of a quadratic equation given in standard form?
  2. What would be the equation if the roots were 77 and 4-4?
  3. How can you expand (x+7)(x4)(x + 7)(x - 4) to write the equation in standard form?
  4. What is the relationship between the coefficients and the roots of a quadratic equation?
  5. How do we verify that x=7x = -7 and x=4x = 4 satisfy the equation (x+7)(x4)=0(x + 7)(x - 4) = 0?

Tip: Remember that the roots of an equation are the values of xx that make each factor equal to zero.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Roots of Equations

Formulas

(x - r1)(x - r2) = 0 for roots r1 and r2

Theorems

Root-Factor Relationship in Quadratic Equations

Suitable Grade Level

Grades 8-10