Question

Write a quadratic equation in the form x² + bx+c=0 that has the following

roots:
Roots: {5,1}

Answer 1

A quadratic equation with roots {5,1} is found by multiplying the factors (x - 5) and (x - 1), which results in the equation x² - 6x + 5 = 0.

Step-by-step explanation:

To write a quadratic equation in the form x² + bx + c = 0 with given roots, you can use the roots to determine the factors of the equation. For the roots {5,1}, the factors would be (x - 5) and (x - 1). To find the quadratic equation, you simply multiply these two factors together.

Here is the calculation:

• (x - 5) * (x - 1) = x² - x - 5x + 5
• Combining like terms gives us x² - 6x + 5

Therefore, the quadratic equation with the roots {5,1} is x² - 6x + 5 = 0.

Answer 2

x^2-6x+5

Step-by-step explanation:

To have roots at x=5 and x=1 you need to write is as follows

(x-5)(x-1)

you then need to multiply these two and get

x^2-6x+5