Question

If L and ß are the zero of
polynomial f(x) = x² + x-2 find the value
of
1/L- 1/B
​

Answer 1

Correct Question:

If α and β are the zero of  polynomial f(x) = x² + x - 2. Find the value  of  1/α - 1/β.

Your Answer:

Given:-

f(x) = x² + x - 2

To Find:-

$\blacktriangleright \tt \frac{1}{\alpha}-\frac{1}{\beta}$

Solution:-

Finding zeroes of f(x)

x² + 2x - x - 2

= x(x+2) - 1(x+2)

= (x-1)(x+2)

To find the zeroes of f(x) we have to equate it with zero

first

x-1=0

x=1

and

x+2=0

x=-2

There can be two cases now

Let α = 1 and β  = -2

So, 1/α - 1/β

= 1 + 1/2

= 3/2

Now let  α = -2 and β = 1

So, 1/α - 1/β

= -1/2 - 1

= -3/2

So, the possible values for 1/α - 1/β is -3/2 and 3/2