School Olympiads - International Mathematics Olympiad (IMO)

Real Numbers, Polynomials & Quadratic Equations question bank (Class 9 & 10 - Advanced Olympiad Problem Solving)

Practice 5 free School Olympiads - International Mathematics Olympiad (IMO) Class 9 & 10 - Advanced Olympiad Problem Solving - Real Numbers, Polynomials & Quadratic Equations questions with answers and step-by-step solutions.

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Q1.

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 5x + 3 = 0$, find the value of $\alpha^3 + \beta^3$.

(A)

{'key': 'A', 'text': '80'}

(B)

{'key': 'B', 'text': '85'}

(C)

{'key': 'C', 'text': '95'}

(D)

{'key': 'D', 'text': '110'}

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Q2.

In an Olympiad competition problem on Real Numbers, Polynomials & Quadratic Equations:
Find the numerical value of $X$ satisfying $$X = (12 \times 5) - 41 + 7$$.

(A)

{'key': 'A', 'text': '26'}

(B)

{'key': 'B', 'text': '30'}

(C)

{'key': 'C', 'text': '22'}

(D)

{'key': 'D', 'text': '35'}

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