If a+b=2 and a4+b4=272 then a quadratic equation whose roots are a and b is

We have,a+b=2 and a4+b4=272 Now, a4+b4=272⇒ a2+b˙22−2a2b2=272⇒ (a+b)2−2ab2−2a2b2=272⇒ (4−2ab)2−2a2b2=272⇒ 16−16ab+2a2b2=272⇒ (ab)2−8(ab)−128=0⇒ (ab−16)(ab+8)=0⇒ab=16 or ,−8Thus, we have a+b = 2 and ab=16, or -8.So, the quadratic equations whose roots are a and b are x2−2x+16=0 and x2−2x−8=0