If alpha beta are the roots of the equation ax {?}^(2) + bx + c = 0 then the quadratic equation whose roots are alpha +beta and alpha beta is ​

Question

If alpha beta are the roots of the equation


`ax {?}^(2) + bx + c = 0`
then the quadratic equation whose roots are alpha +beta and alpha beta is
​

Answer 1

Explanation:

Hello, I believe that we can consider a different from 0.

By definition of the roots we can write.

`ax^2+bx+c=a(x-\alpha)(x-\beta)=a(x^2-(\alpha + \beta)x+\alpha \cdot \beta)\\\\\text{So we can say that:}\\\\\alpha + \beta = (-b)/(a)\\\\\alpha \cdot \beta=(c)/(a)\\\\\text{So the expected quadratic equation is}\\\\(x+(b)/(a))(x-(c)/(a))=0\\\\<=> \Large \boxed{\sf \bf \ (ax+b)(ax-c)=0 \ }`

Thank you