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Intermediate 2nd Year Maths 2A Binomial Theorem Quiz
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Intermediate 2nd Year Maths 2A Binomial Theorem Quiz

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Questions and Answers

What is the expansion of $(x + a)^n$?

  • $nC0 \cdot a^n + nC1 \cdot a^{n-1} + nC2 \cdot a^{n-2} + ... + nCn \cdot a^0$
  • $nC0 \cdot x^n + nC1 \cdot x^{n-1} + nC2 \cdot x^{n-2} + ... + nCn \cdot x^0$
  • $nC0 \cdot x^n \cdot a + nC1 \cdot x^{n-1} \cdot a + nC2 \cdot x^{n-2} \cdot a + ... + nCn \cdot x \cdot a^n$
  • $nC0 \cdot x^n \cdot a^0 + nC1 \cdot x^{n-1} \cdot a^1 + nC2 \cdot x^{n-2} \cdot a^2 + ... + nCn \cdot x^0 \cdot a^n$ (correct)

    • What are the coefficients in the expansion of $(x + a)^n$ called?

  • Polynomial coefficients
  • Trigonometric coefficients
  • Exponential coefficients
  • Binomial coefficients (correct)

    • How many terms are there in the expansion of $(x + a)^n$?

  • $2n$
  • $2n + 1$
  • $n + 1$ (correct)
  • $n^2$

    • What is the number of terms in the expansion of $(a + b + c)^n$?

    <p>$\frac{(n+1)(n+2)}{2}$</p> Signup and view all the answers

    What is the middle term in the expansion of $(x + a)^n$ if $n$ is even?

    <p>$T\left(\frac{n}{2}+1\right)$</p> Signup and view all the answers

    What is a polynomial?

    <p>An expression consisting of one or more terms</p> Signup and view all the answers

    What does the theory of equations study?

    <p>Algebraic equations defined by a polynomial</p> Signup and view all the answers

    What is the relationship between the roots and coefficients of a quadratic equation?

    <p>The sum of product of roots taken two at a time is the coefficient of x</p> Signup and view all the answers

    What is the product of roots for a cubic equation?

    <p>It is equal to the constant term</p> Signup and view all the answers

    If one root of a cubic equation is double of another, then find all the roots of equation $x^3 + 36 = 7x^2$.

    <p>6, 6, 0</p> Signup and view all the answers

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