MP Board · Class 10 · Mathematics · PolynomialsIf the zeroes of the quadratic polynomial $ax^2 + bx + c$ are both positive, then:
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Total Attempts: 12
Accuracy Rate: 41.7%
Step-by-Step Solution
Let the zeroes be $\alpha$ and $\beta$. Both are positive, so $\alpha + \beta > 0$ and $\alpha\beta > 0$. \nSum of zeroes = $-b/a > 0$\nProduct of zeroes = $c/a > 0$\nThis implies that $a$, $b$, and $c$ must have signs such that $b/a < 0$ and $c/a > 0$, meaning $a$ and $c$ have the same sign, and $b$ has the opposite sign of $a$.
Detailed Options Breakdown
Option : a, b and c all have the same sign
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 1: a and c have same sign, b has opposite sign (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: b and c have same sign, a has opposite sign
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 3: a and b have same sign, c has opposite sign
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.