find the sum of the roots

Question

3X² - 2X + 5 = 1

Answer 1

There's another way to do this, without actually calculating the roots.

 

The sum of the roots of a quadratic polynomial is always equal to -b/a, no matter what the actual roots are.

 

So in this case, you have -b/a = -(-2) / 3 = 2/3.

 

You can see this by starting with the quadratic formula:

 

x = (-b ± √(b² - 4ac)) / 2a

 

That means that there are two roots: (-b + √(b² - 4ac)) / 2a and (-b - √(b² - 4ac)) / 2a

 

Add these together. 

 

(-b + √(b² - 4ac)) / 2a + (-b - √(b² - 4ac)) / 2a

= (-b + √(b² - 4ac) + -b - √(b² - 4ac)) / 2a

 

The terms with the square root cancel out and you get (-b + -b) / 2a = -2b/2a = -b/a

Answer 2

3x² - 2x + 5 = 1

 

3x² - 2x + 4 = 0

 

Use the quadratic formula:

 

x = (-b±√(b²-4ac))/2a

x = 1/3 ± i(1/3)√11

 

Sum of the roots = 1/3 + i(1/3)√11 + 1/3 - i(1/3)√11 = 2/3