Gr 10 Math Ch 2: Solving Quadratic Equations
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Questions and Answers

What is the maximum number of solutions a quadratic equation can have?

  • No solutions
  • Two solutions (correct)
  • Three solutions
  • One solution

    • Which step is NOT part of solving a quadratic equation?

  • Check the solution
  • Factorise the quadratic expression
  • Divide by common factors
  • Graph the equation on a coordinate plane (correct)

    • In the equation $3x^2 + 6x + 3 = 0$, what is the first necessary step to simplify it?

  • Rewrite in standard form
  • Divide by a common factor (correct)
  • Set the equation equal to 1
  • Factor the equation directly

    • What does it mean for a quadratic equation to be balanced?

    <p>The same operation must be applied to both sides of the equation</p> Signup and view all the answers

    What is the correct form a quadratic equation must be in for solving?

    <p>$ax^2 + bx + c = 0$</p> Signup and view all the answers

    After factorising the expression $(2x + 3)(x - 1) = 0$, what should you do next?

    <p>Set each factor equal to zero</p> Signup and view all the answers

    What is the purpose of factorising a quadratic equation?

    <p>To find the solutions by setting factors equal to zero</p> Signup and view all the answers

    Which of the following statements about quadratic equations is correct?

    <p>Quadratic equations can have zero, one, or two solutions.</p> Signup and view all the answers

    When given the quadratic equation $x^2 + 4x + 4 = 0$, what will be the first step in solving it?

    <p>Factorise it into $(x + 2)(x + 2) = 0$</p> Signup and view all the answers

    How can you verify the solutions obtained from a quadratic equation?

    <p>By substituting the solutions back into the original equation</p> Signup and view all the answers

    What does it mean for a quadratic equation to be balanced?

    <p>Any operation performed on one side must also be performed on the other side</p> Signup and view all the answers

    Which of the following is NOT a step in solving a quadratic equation?

    <p>Finding common roots with linear equations</p> Signup and view all the answers

    What is a characteristic of a quadratic equation compared to a linear equation?

    <p>A quadratic equation can have at most two solutions.</p> Signup and view all the answers

    Which step in the method of solving quadratic equations involves checking the initial format of the equation?

    <p>Rewrite the Equation</p> Signup and view all the answers

    What is an essential aspect of maintaining the integrity of a quadratic equation during manipulation?

    <p>Perform the same operation on both sides to keep it balanced.</p> Signup and view all the answers

    What can occur if factorisation is improperly performed on a quadratic equation?

    <p>The values will no longer satisfy the original equation.</p> Signup and view all the answers

    Which of the following statements best describes the final step in solving a quadratic equation?

    <p>Substitute the obtained values back into the original equation.</p> Signup and view all the answers

    When factorising the quadratic expression $3x^2 + 12x + 9 = 0$, which step should precede the factorisation process?

    <p>Divide by the common factor of the coefficients.</p> Signup and view all the answers

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