What is the roots of quadratic function?

Question

What means by 'Let α and β be the roots of quadratic function ax² +bx+c=0'

And talk about the sum of roots and product of roots...I don't even know how α and β pop out,isn't the roots means the solution or means 'x'?

And later it tells that 'The quadratic equation with α and β as roots is x² - (α+β)x + αβ = 0.'

 

Answer 1

If α and β are roots of the equation then (x - α) and (x - β) are factors of the polynomial.

This is always true.

 

For the last statement, the factors are (x - α) and (x - β), as stated above.

Then the polynomial is (x - α)(x - β) = 0

Now multiply that out and you shall see the equation given.