Question

7. If a & B are zeroes of quadratic polynomial x²- ax + b then find value of a² +b² .​

Answer 1

Answer:

If α and β are the roots of x²–ax+b.

Then,

Sum of roots (α+β)=-(coefficient of x)/coefficient of x²=-(-a)/1 = a.

Product of roots(αβ)=(constant term)/coefficient of x²= b/1 = b.

Then,

α²+β²=(α+β)²–2αβ=a²–2b and

α³+β³=((α+β)(α²+β²–αβ)=a.(a²–2b–b)=a.(a²–3b)

So,

(α/β² + β/α²) =(α³+β³)/((α².β²)=a.(a²–3b)/b²,Ans.

I hope it helps you…!!!