Question

If α and β are the roots of the polynomial x2 -4x+5 then α+β is ​

Answer 1

Answer:

Solution:

Since, α and β are roots of the quadratic equation

x2−4x+5=0

So, α+β=4 and αβ=5 ... (i)

Now, (α2+β)+(α+β2)=(α2+β2)+(α+β)

=(α+β)2−2αβ+(α+β)

=16−10+4=10

and (α2+β)(α+β2)=α3+α2β2+βα+β3

=α3+β3+αβ(αβ+1)

=(α+β)(α2+β2−αβ)+αβ(αβ+1)

=(α+β)[(α+β)2−3αβ]+αβ(αβ+1)

=4[16−15]+5(5+1)

=4+30=34

So, the quadratic equation whose roots are

(α2+β) and (α+β2) is

x2−(α2+β+α+β2)x+(α2+β)(α+β2)=0

⇒x2−10x+34=0

Step-by-step explanation: