Question

If alpha and beta are the zeroes of quad .Poly. 5x^2 -3x +2, then find the quad. Poly. Whose zeroes are alpha÷beta + beta÷alpha -alphabeta

Answer 1

ANSWER=2X^2-3X+4

SOLUTION STEP BY STEP

the zeroes are alpha and beta.

formula-x^2-(sum of zeroes )x+(product of zeroes)

sum of zeroes=alpha+beta=3........(1)

product of zeroes=alpha*beta=2...(2)

For new polynomial-

zeroes are-

1.)1/alpha+1/beta

2) alpha*beta

1/alpha +1/beta

={taking LCM alpha beta)

=(alpha+beta)/alpha.beta

=3/2.....…................................(3)

alpha .beta

=2....................................................(4)

polynomial=k(x^2 - sum of zeroes.x + product of zeroes)

=k(x^2-3x/2+2)

k=2

p(x)=2x^2-3x+4