Question

If α and β are the roots of the equation x²+x-7=0 ,form the equation whose roots are α² and β²

Answer 1

Answer:

If a and β are the roots of the equation x2+x–1=0 , then what is the equation whose roots are α5 and β5 ?

α+β=−1andαβ=−1

Since α is a root

α2+α–1=0......(1)

α3+α2–α=0.....(2)

α4+α3–α2=0....(3)

α5+α4–α3=0......(4)

(4)−(3)+2(2)−3(1)gives

α5−5α+3=0

Similarly β5−5β+3=0

Adding α5+β5−5(α+β)+6=0

⟹α5+β5=−5−6=−11

α5β5=(−1)5=−1

So the equation having α5,β5 as roots

x2−(−11)x−1=0or

x2+11x−1=0

Answer 2

check for calculatio। mistake

hope you got it

all the best