Let the smaller and greater number be a and b respectively Given a+b=75⇒b=75−a Also a×(b−15)=900 ⇒a×(75−a−15)=900 ⇒a(60−a)=900 ⇒a2−60a+900=0 ⇒(a−30)2=0 ⇒a=30,b=75−a=45 As per the question, roots of the quadratic equation are a=
a
2
and β=
b
5
∴α=15 and β=9 Equation is: (x−15)(x−9)=0 ⇒x2−24x+135=0