Finding Quadratic Polynomials from Sums and Products of Zeroes
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Questions and Answers

What is the geometric meaning of the zeroes of a polynomial?

  • Minimum points of the polynomial
  • Values of x where the polynomial crosses the x-axis (correct)
  • Values that make the polynomial equal to zero only
  • Maximum points of the polynomial

    • In the given text, when x = 3, what is the value of x^2 - 3?

  • 9
  • 6
  • 12
  • 3 (correct)

    • What is the relationship between the sum and product of the zeroes of a quadratic polynomial?

  • They are always equal
  • Their sum and product are both zero
  • The sum is equal to the coefficient of x and the product is equal to the constant term (correct)
  • Their difference is equal to the coefficient of x

    • What is a possible quadratic polynomial with sum of zeroes as -3 and product of zeroes as 2?

    <p>x^2 + 3x + 2 (D)</p> Signup and view all the answers

    In the cubic polynomial p(x) = 2x^3 - 5x^2 - 14x + 8, if x = -2, what is the value of p(x)?

    <p>-16 (B)</p> Signup and view all the answers

    What is the relation between the sum and product of the zeroes of a cubic polynomial?

    <p>Their product is equal to the constant term in the polynomial (D)</p> Signup and view all the answers

    What is one possible quadratic polynomial that fits the conditions mentioned in Example 4?

    <p>-x^2 + 4x + 6 (B)</p> Signup and view all the answers

    What are the zeroes of the quadratic polynomial x^2 + 3x + 2?

    <p>-1 and -2 (D)</p> Signup and view all the answers

    The quadratic polynomial given in the text is 3x^2 - 5x - 11.

    <p>False (B)</p> Signup and view all the answers

    The sum of the zeroes of the quadratic polynomial 3x^2 - 5x - 11 is 3.

    <p>False (B)</p> Signup and view all the answers

    The product of the zeroes of the quadratic polynomial 3x^2 - 5x - 11 is -3.

    <p>True (A)</p> Signup and view all the answers

    The zeroes of the quadratic equation x^2 - 2x - 8 are 4 and -2.

    <p>False (B)</p> Signup and view all the answers

    The sum of the zeroes of the quadratic polynomial 6x^2 - 3 - 7x is 6.

    <p>False (B)</p> Signup and view all the answers

    The product of the zeroes of the quadratic polynomial t^2 - 15 is -15.

    <p>True (A)</p> Signup and view all the answers

    The quadratic polynomial 4u^2 + 8u has one zero as u = -1.

    <p>True (A)</p> Signup and view all the answers

    The sum of the zeroes of the quadratic equation 4s^2 - 4s + 1 is 0.

    <p>True (A)</p> Signup and view all the answers

    The product of the zeroes of the quadratic polynomial 3x^2 - x - 4 is -4.

    <p>False (B)</p> Signup and view all the answers

    The sum of the coefficients of the quadratic polynomial x^2 - 2x - 8 is -10.

    <p>True (A)</p> Signup and view all the answers

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