Question

If the roots of the quadratic equation \( 2x^2 - 8x + 5 = 0 \) are \( p \) and \( q \), find the value of \( \frac{1}{p} + \frac{1}{q} \).

• A. \( 4 \)
• B. \( \frac{8}{5} \)
• C. \( \frac{5}{2} \)
• D. \( 2 \)

Hint:

To find \( \frac{1}{p} + \frac{1}{q} \) for the roots of a quadratic equation, use \( \frac{p + q}{pq} \), where \( p + q \) and \( pq \) are the sum and product of the roots.

Answer 1

The Correct Option is B

The given quadratic equation is \( 2x^2 - 8x + 5 = 0 \). For a quadratic equation \( ax^2 + bx + c = 0 \), the sum and product of the roots are: 
Sum of roots: \( p + q = -\frac{b}{a} \) 
Product of roots: \( pq = \frac{c}{a} \) Here, \( a = 2 \), \( b = -8 \), \( c = 5 \). Thus: \[ p + q = -\frac{-8}{2} = 4 \] \[ pq = \frac{5}{2} \] To find \( \frac{1}{p} + \frac{1}{q} \), use the identity: \[ \frac{1}{p} + \frac{1}{q} = \frac{p + q}{pq} \] Substitute the values: \[ \frac{1}{p} + \frac{1}{q} = \frac{4}{\frac{5}{2}} = 4 \cdot \frac{2}{5} = \frac{8}{5} \] Thus, the value of \( \frac{1}{p} + \frac{1}{q} \) is: \[ {\frac{8}{5}} \]