Question

if a and b are the zeros of a polynomial x^2 -2x -3 find 1/a +1/B

Answer 1

Step-by-step explanation:

Hi,

P ( x ) = X² - 2X - 3.

X² - 3x + x - 3 = 0

x ( x - 3 ) + 1 (x - 3 )= 0

( x - 3 ) ( x + 1 ) = 0

( x - 3 ) = 0 or ( x + 1 ) = 0

X = 3 or x = -1

Therefore,

3 and -1 are the two zeroes of the given quadratic polynomial.

Now,

Sum of zeroes = a + b = 3 + (-1) = 2

And , Product of the zeroes = 3 × -1 = -3.

Therefore,

1/a + 1/B

=> B + a / ab

=> 2 / -3

=> -2/3

Hence,

1/a + 1/b = -2/3

Hope it will help you :)