Question

if alpha and beta are the zeroes of the polynomial f(x)=4x²-5x+1, find a quadratic polynomial whose zeroes are alpha²/beta and beta²/alpha​

Answer 1

Answer:

16x²-65x+4=0

Step-by-step explanation:

a=4, b=-5, c=1

a+b=-b/a=5/4

ab=c/a=1/4

sum of roots

a²/b +b²/a =a³+b³/a+b

=(a+b)³-3(ab)(a+b)/ab

=(5/3)³-3(1/4)(5/4) /1/4

=65/16

product of roots

a²/b ×b²/a =ab=1/4

…NEW EQUATION

x²-(a+b)x+ab=0

x²-65/16x+1/4

multiply through by the L.C.M of 16 and 4

16x²-65x +4=0

I hope it is clear enough. I am from Nigeria by the way.