Question

If \( x \) satisfies the equation \( 3x^2 - 7x + 2 = 0 \), then what is the value of \( \frac{1}{x_1} + \frac{1}{x_2} \), where \( x_1 \) and \( x_2 \) are the roots?

• A. \( \frac{7}{3} \)
• B. \( \frac{3}{7} \)
• C. \( \frac{7}{2} \)
• D. \( \frac{2}{7} \)

Hint:

Use the identity \( \frac{1}{x_1} + \frac{1}{x_2} = \frac{x_1 + x_2}{x_1 x_2} \) for reciprocal root expressions in quadratics. Vieta's formulas are your go-to tool here.

Answer 1

The Correct Option is C

Step 1: Use the identity for the sum of reciprocals of roots.
We are given the quadratic equation:
3x² - 7x + 2 = 0
Let the roots be x₁ and x₂. We need to calculate:
1/x₁ + 1/x₂ = (x₁ + x₂) / (x₁ × x₂)

Step 2: Apply Vieta’s formulas.
For any quadratic equation ax² + bx + c = 0:

• Sum of roots x₁ + x₂ = -b/a = -(-7)/3 = 7/3
• Product of roots x₁ × x₂ = c/a = 2/3

 

Step 3: Substitute the values into the formula.
(x₁ + x₂) / (x₁ × x₂) = (7/3) / (2/3) = (7/3) × (3/2) = 7/2

Final Answer: 7/2