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Intermediate 2nd Year Maths 2A Binomial Theorem Quiz

10 Questions

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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 $(a + b + c)^n$?

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

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

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

What is a polynomial?

An expression consisting of one or more terms Signup and view all the answers

What does the theory of equations study?

Algebraic equations defined by a polynomial Signup and view all the answers

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

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

What is the product of roots for a cubic equation?

It is equal to the constant term Signup and view all the answers

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

6, 6, 0 Signup and view all the answers