NCERT · Class 10 · Mathematics · PolynomialsIf $\alpha$ and $\beta$ are the zeroes of the polynomial $2x^2 - 5x + 7$, then the value of $\frac{1}{\alpha} + \frac{1}{\beta}$ is:
Step-by-Step Solution
For the polynomial $2x^2 - 5x + 7$, $a = 2$, $b = -5$, $c = 7$.\nSum of zeroes: $\alpha + \beta = -\frac{b}{a} = \frac{5}{2}$\nProduct of zeroes: $\alpha\beta = \frac{c}{a} = \frac{7}{2}$\nNow, $\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha\beta} = \frac{5/2}{7/2} = \frac{5}{7}$.
Detailed Options Breakdown
Option : $\frac{5}{7}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $-\frac{5}{7}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 2: $\frac{7}{5}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 3: $-\frac{7}{5}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
💡 Study Guide: This question tests core syllabus concepts from Polynomials. For formulas, key summaries, and mock exam reference guides, read the full Polynomials Revision Notes.