Question

If alpha and beta are zeroes of qudratic polynomial f(x) = x²+x-6 then polynomial whose zeroes are 2 alpha + 1 and 2 beta + 1 ...​

Answer 1

Answer:

LET ALPHA = A AND BETA = B

A + B = -1

AB = -6

SUM OF ROOTS =

2A+1+2B+1

= 2A+2B+2

= 2(A+B)+2

= 2(-1)+2

-2+2

= 0

PRODUCT OF ROOTS =

(2A+1)(2B+1) = 4AB +2A+2B+1

= 4AB +2(A+B) +1

= 4(-6)+2(-1)+1

= -24-2+1

= -25

POLYNOMIAL WITH 2A+1 AND 2B+1 AS ZEROS

IS X² - X ( 2A+1+2B+1) + (2A+1)(2B+1)

X²-X(SUM OF ROOTS) + PRODUCT OF ROOTS

X²- X(0) + (-25)

X²-25