Question

If alpha and beta are the zeroes of the quadratic polynomial, f(x)=x^2-1. Find a quadratic polynomial whose zeroes are 2×alpha÷beta and 2×beta÷alpha.

Answer 1

Ans-x^2-4x+4
Step by step explanation in the above picture

Answer 2

Answer:

Step-by-step explanation:

f(x)= x square - 1

Sum of zeroes = alfa+ beta = -b/. a = 0/1 = 0

product of zeroes

= alfa ×. beta = c/ a = 1/1 = 1

Now the zeroes of reqd polynomial are 2alfa/beta and 2 beta / alfa

Sum of zeroes = 2alfa/ beta + 2 beta,/ alfa

= 2 alfa square + 2 beta square/alfa × beta

= 2 ( alfa square + beta square)/alfa × beta

= 2 [(alfa + beta)^2 - 2 alfa beta]/alfa beta

= 2[(0)^2-2 × 1 ]/1

=2[0-2]/1

=-4

Product of zeroes = 2alfa/beta ×2 beta/ alfa

=2×2 = 4

Hence reqd polynomial is

x square - (alfa+beta)x + alfa beta

= x square -(-4)x + 4

= x square + 4x + 4