Question

if alpha and beta are the zeroes of the quadratic polynomial x2-5x+6, then find a quadratic polynomial whose zeroes are alpha2/beta and beta2/alpha​

Answer 1

Answer:

2x^2 - 5x + 3

Step-by-step explanation:

x2 - 5x + 6

alpha + beta = -b/a = 5/1 = 5

alpha*beta = c/a = 6/1 = 6

Now if zeroes are halved then,

alpha/2 + beta/2 = 5/2

alpha/2 * beta/2 = (alpha*beta)/4 = 6/4 = 3/2

Based on above two equations, we can conclude,

New a = 2

New b = -5

New c = 3

New equation = 2x^2 - 5x + 3