Question

If alpha and beta are the zeros of the quadratic polynomial x2-x-2 find a polynomial whose zeros are 2alpha+1 and 2bita-1

Answer 1

Let @ is alpha.


Here,
Polynomial = x² - x -2

@ + ß = -b/a = -(-1)/1 = 1

@ß = c/a = -2/1 = -2


we need to find a new polynomial whose zeroes are 2@ +1 and 2ß - 1.

Sum of zeries = (2@+1) + (2ß-1)
= 2@ + 2ß
= 2(@+ß)
= 2(1)
= 2

Product of zeroes
= (2@ + 1)(2ß - 1)
= 4@ß -2@ + 2ß -1
= 4(-2) -2(1) - 1
= -8 - 2 - 1
= -11


We know that,

Q.P. = x² - (@+ß)x + (@ß)
= x² -2x - 11



Hence, this is the required polynomial.


Hope it helps