finding the equation

Question

find the equation with roots (1+/5) and (1-/5)    *note /5 means square rootand the point (2,5)

Answer 1

(x-1-√5)(x-1+√5)=x^2-2x+1-5=x^2-2x-4=0 is a quadratic with the given roots. The general quadratic with the same roots is a(x^2-2x-4)=0 and we're told (2,5) is satisfied by the quadratic y=a(x^2-2x-4); 5=a(4-4-4)=-4a so a=-5/4 and the quadratic is y=(-5/4)(x^2-2x-4) or 4y=20+10x-5x^2 or 4y=5(4+2x-x^2), etc.