Question

If alpha and beta are the two zeroes of the polynomial x^2 - 3x + 1 , then find a quadratic polynomial whose zeroes are 1/alpha^2 and 1/ beta ^2​

Answer 1

Answer:

x² - x + 1

For explaination , please refer to the attachment.

Note:

• If A and B are the zeros of the a quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , A•B = c/a

• If A and B are the zeros of any quadratic polynomial , then it is given as ;

x² - (A+B)x + A•B.