1. Find the quadratic equation whose roots are Alpha = 3, Beta = -4

Solution:
Let `alpha=3` and `beta=-4`

Then, the sum of the roots `= alpha+beta=(3)+(-4)=-1`

and the product of the roots `= alpha*beta=(3)*(-4)=-12`

The equation with roots `alpha` and `beta` is given by

`x^2-(alpha+beta)x+alpha*beta=0`

`:.x^2-(-1)x+(-12)=0`

`:.x^2+x-12=0`