Solving Quadratic Equations Quiz
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Questions and Answers

If one root of the equation x^2 + mx - 5 = 0 is 2, what is the value of m?

  • $9$
  • $-9$
  • $-8$ (correct)
  • $8$
  • What is the discriminant of the quadratic equation 2y^2 - y + 2 = 0?

  • $49$
  • $-15$
  • $-23$
  • $-31$ (correct)
  • Which of the following sets of roots can form a quadratic equation?

  • {10, -10}
  • {1+3√5, 1-3√5}
  • {-5, 7}
  • {0, 7} (correct)
  • What is one possible quadratic equation for which the roots are 10 and -10?

    <p>$x^2 - 100 = 0$</p> Signup and view all the answers

    For which equation do the roots have a sum of 5 and a sum of their cubes equal to 35?

    <p>$x^2 - 5x + 6 = 0$</p> Signup and view all the answers

    What is the solution to the equation (m - 12)x^2 + 2(m - 12)x + 2 = 0 to have real and equal roots?

    <p>$m = -6$</p> Signup and view all the answers

    If Mukund possesses `50 more than Sagar, what could be a suitable quadratic equation representing their possessions?

    <p><code>m(s+50) = 0</code></p> Signup and view all the answers

    What is the nature of roots for the quadratic equation 3x^2 - 5x + 7 = 0?

    <p>Complex conjugates</p> Signup and view all the answers

    Which equation has real and equal roots when solved?

    <p><code>x^2 - 3x +1=0</code></p> Signup and view all the answers

    One of the roots of equation x^2 + mx - 5 = 0 is 2; find m. Which distractor correctly provides m?

    <p>-9</p> Signup and view all the answers

    Study Notes

    Quadratic Equations

    • A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (x) is two.
    • The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

    Solving Quadratic Equations Using Formula

    • The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.
    • The formula can be used to solve quadratic equations of the form ax^2 + bx + c = 0.

    Nature of Roots of a Quadratic Equation

    • The nature of roots of a quadratic equation depends on the value of b^2 - 4ac, which is called the discriminant (∆).
    • If ∆ > 0, the roots are real and unequal.
    • If ∆ = 0, the roots are real and equal.
    • If ∆ < 0, the roots are not real.

    Discriminant (∆)

    • The discriminant (∆) is b^2 - 4ac.
    • It determines the nature of roots of a quadratic equation.

    Examples and Practice Exercises

    • Various examples and practice exercises are provided to illustrate the concepts of quadratic equations.
    • These include solving quadratic equations, finding the value of the discriminant, determining the nature of roots, and more.

    Trapezium and Quadratic Equation

    • A trapezium is a quadrilateral with two pairs of opposite sides.
    • The area of a trapezium can be found using the formula: Area = (sum of parallel sides) * height / 2.
    • A quadratic equation can be used to find the length of the parallel sides.

    Problem Set

    • A set of practice exercises is provided to test understanding of quadratic equations.
    • The exercises cover a range of topics, including solving quadratic equations, finding the value of the discriminant, determining the nature of roots, and more.

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    Description

    Test your knowledge of solving quadratic equations using formulas and flow charts. Practice solving equations with different coefficients and identify the values of a, b, c to find the roots. Includes examples like x² - 7x + 5 = 0 and 2m² = 5m - 5.

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