Value of an Expression Using Zeros of a Quadratic Polynomial

Video Explanation

Question

If \( \alpha \) and \( \beta \) are the zeroes of the quadratic polynomial

\[ f(x) = x^2 + x – 2, \]

find the value of

\[ \frac{1}{\alpha} – \frac{1}{\beta}. \]

Solution

Step 1: Find the Zeros of the Polynomial

Factorising:

\[ x^2 + x – 2 = (x + 2)(x – 1) \]

So, the zeroes are:

\[ \alpha = 1,\quad \beta = -2 \]

Step 2: Evaluate the Required Expression

\[ \frac{1}{\alpha} – \frac{1}{\beta} = \frac{1}{1} – \frac{1}{-2} \]

\[ = 1 + \frac{1}{2} \]

\[ = \frac{3}{2} \]

Conclusion

The required value is:

\[ \boxed{\frac{3}{2}} \]

\[ \therefore \quad \frac{1}{\alpha} – \frac{1}{\beta} = \frac{3}{2}. \]