Polynomials MCQ: Answers and Explanation

The name "polynomial" comes from the words "poly" (meaning many) and "nomial" (meaning phrase), so it means "many terms."

• A polynomial is made up of solely added, subtracted, and multiplied terms.
• ax² + bx + c is the form of a quadratic polynomial in x with real coefficients, where a, b, and c are real numbers with a = 0.
• The degree of a polynomial refers to the variable's highest exponent in the polynomial. 2x² + 4 is an example where the degree is 2.
• Linear, quadratic, and cubic polynomials have the degrees 1, 2, and 3 polynomials, respectively.
• A polynomial can have terms with constants such as 5, -2, and others, as well as variables like x and y and exponents such as 2 in y².
• Addition, subtraction, and multiplication can be used to combine these, but not division.
• The x-coordinates of the locations where the graph of y = p(x) contacts the x-axis are the zeroes of polynomial p(x).
• If α and β are the zeroes of the quadratic polynomial ax² + bx + c, then:

• If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d = 0, then:

• Zeroes, also known as α, β, γ, follow the rules of algebraic identities, i.e.,

(α + β)² = α² + β² + 2αβ

∴(α² + β²) = (α + β)² – 2αβ

• If p(x) and g(x) are any two polynomials with g(x) = 0, then p(x) = g(x) * q + r is the division algorithm:

Dividend = Divisor x Quotient + Remainder

The video below explains this:

Polynomials Detailed Video Explanation:

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Question 1: If the zeroes of the quadratic polynomial ay² + by + c, c ≠ 0 are equal, then

1. c and b have opposite signs
2. c and a have opposite signs
3. c and b have the same signs
4. c and a have the same signs

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Question 2: If the sum of zeroes of the quadratic polynomial 3x² – kx + 6 is 3, then the value of k is:

1. 4
2. 5
3. 7
4. 9

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Question 3: The degree of the polynomial, x5 – 2x2 + 2 is:

1. 2
2. 4
3. 1
4. 5

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Question 4: If p(x) is a polynomial of degree one and p(y) = 0, then y is said to be:

1. Zero of p(x)
2. Value of p(x)
3. Constant of p(x)
4. None of the above

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Question 5: A polynomial's zeros can be represented graphically. The number of polynomial zeros equals the number of points on the graph of the polynomial:

1. Intersects y-axis
2. Intersects x-axis
3. Intersects y-axis or x-axis
4. None of the above

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Question 6: A polynomial of degree p has:

1. Only one zero
2. At least p zeroes
3. More than p zeroes
4. At most p zeroes

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Question 7: If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then the polynomial is:

1. x² + 6x + 5 = 0
2. x² + 6x - 5 = 0
3. x² - 6x + 5 = 0
4. x² - 6x - 5 = 0

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Question 8: Zeros of p(x) = x² - 27 are:

1. ± 3√3
2. ± 9√3
3. ± 7√3
4. None of the above

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Question 9: The quadratic polynomial whose zeroes are 3 + √2 and 3 – √2 is:

1. x² – 6x - 7
2. x² + 6x + 7
3. x² – 6x + 7
4. x² + 6x - 7

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Question 10: If a quadratic polynomial's discriminant, D, is greater than zero, the polynomial has:

1. two real and equal roots
2. two real and unequal roots
3. imaginary roots
4. no roots

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