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?
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?
Show 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.
Updated On: Mar 18, 2026
- \( \frac{7}{3} \)
- \( \frac{3}{7} \)
- \( \frac{7}{2} \)
- \( \frac{2}{7} \)
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The Correct Option is C
Solution and Explanation
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
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