Question

Use vieta's formulas to find the sum and the product of the roots of the equation: x^2-210x=0

Answer 1

Sure! First, we need to recognize that this is a quadratic equation in the form of ax^2 + bx + c = 0 where a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.

Let's break down our given equation which is x^2-210x=0. In this equation:

a = 1 (coefficeint of x^2)

b = -210 (coefficeint of x)

c = 0 (constant term)

According to the properties of quadratic equations, specifically Vietas's formulas, the sum of the roots of the equations is equal to -b/a and the product of the roots is equal to c/a.

So, we can calculate the sum and product of roots as follows:

Sum of Roots = -b/a = -(-210)/1 = 210

Product of Roots = c/a = 0/1 = 0

Therefore, the sum of roots of the equation x^2-210x=0 is 210, and the product of roots is 0.

Answer 2

sum of the roots:
`x_1+x_2=0`

product of the roots:
`x_1x_2=-210`

Explanation:

`x^2-210=0\quad\implies\quad a=1\,,\ b=0\,,\ c=-210\\\\b^2-4ac=0-(-810)=810>0`

From Vieta's formulas applied to quadratic polynomial we have:

if
`b^2-4ac\geqslant0` then

sum of roots:
`x_1+x_2=-\frac ba=-\frac{0}2=0`

product of the roots:
`x_1x_2=\frac ca=\frac{-210}1=-210`