Solving Quadratic Equations by Factoring
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Questions and Answers

What is the first step to solve a quadratic equation using the completing the square method?

  • Divide the equation by the coefficient of x^2 (correct)
  • Factor the quadratic equation
  • Convert the equation to the form of difference of two squares
  • Identify the roots of the equation

    • In the quadratic equation x^2 - 5x - 3 = 0, what are the roots of the equation?

  • x = -5 or x = 3
  • x = 5 or x = 3
  • x = 5 or x = -3 (correct)
  • x = 3 or x = -5

    • What is the solution to the quadratic equation x^2 + 8x - 48 = 0?

  • x = -4 or x = 12
  • x = -16 or x = 14
  • x = 4 or x = -12 (correct)
  • x = 16 or x = -14

    • For which of the following equations would completing the square method be most appropriate?

    <p>m^2 - 5m = -3</p> Signup and view all the answers

    What is the intermediary step when solving x^2 + 8x - 48 = 0 using factorization?

    <p>(x + 4)^2 - 64 = 0</p> Signup and view all the answers

    What is a key advantage of converting a quadratic equation to a form of difference of two squares?

    <p>Simplifies factorization of the equation</p> Signup and view all the answers

    In the first example given, what is the solution for x and y in the simultaneous equations 5x - 3y = 8 and 3x + y = 2?

    <p>(x, y) = (1, -1)</p> Signup and view all the answers

    Which of the following is a quadratic equation?

    <p>$x(x + 5) = 2$</p> Signup and view all the answers

    What is the method used to solve the simultaneous equations in the second example given?

    <p>Addition method</p> Signup and view all the answers

    Which of the following is NOT a quadratic equation?

    <p>$5x^2 = 90$</p> Signup and view all the answers

    When solving 3x + 2y = 29 and 5x - y = 18, what is the correct solution for x and y?

    <p>(x, y) = (8, -3)</p> Signup and view all the answers

    If the roots of $x^2 + kx + k = 0$ are real and equal, what is the value of k?

    <p>0</p> Signup and view all the answers

    What is the result of multiplying equation (II) by 2 in the second example given?

    <p>-10x + 2y = 36</p> Signup and view all the answers

    For $2x^2 - 5x + 2 = 0$, what is the value of the discriminant?

    <p>17</p> Signup and view all the answers

    In the third example provided, what happens to the coefficients of x and y in the two equations?

    <p>They are interchanged</p> Signup and view all the answers

    Which of the following quadratic equations has roots 3 and 5?

    <p>$x^2 - 8x + 15 = 0$</p> Signup and view all the answers

    What is the correct value of x when solving 15x + 17y = 21 and 17x + 15y = 11?

    <p>x = -3</p> Signup and view all the answers

    Out of the following equations, which one has the sum of its roots as -5?

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

    What is the formula used to solve a quadratic equation according to the text?

    <p>$2a - b - \frac{b^2 - 4ac}{2a}$</p> Signup and view all the answers

    Which expression represents one of the roots of a quadratic equation?

    <p>$-\frac{b}{2a} - \sqrt{\frac{b^2-4ac}{2a}}$</p> Signup and view all the answers

    From the given text, how are the values 'a' and 'b' related?

    <p>a and b are unrelated in the context</p> Signup and view all the answers

    What happens to the roots of a quadratic equation if a root is represented by 'a'?

    <p>Both roots become equal</p> Signup and view all the answers

    What is the relationship between 'a', 'b', and 'c' in the context of solving a quadratic equation?

    <p>$ab = c$</p> Signup and view all the answers

    How does the formula $2ax = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ help in solving quadratic equations?

    <p>It assists in finding the discriminant</p> Signup and view all the answers

    In an arithmetic progression, what is the nth term formula?

    <p>$a_n = a + (n-1)d$</p> Signup and view all the answers

    In an arithmetic progression, if the first term is 3 and the common difference is 5, what is the 6th term?

    <p>28</p> Signup and view all the answers

    What is the sum of the first 10 terms of an arithmetic progression with a first term of 2 and a common difference of 3?

    <p>85</p> Signup and view all the answers

    How many oranges would each student receive if Ranjana distributed them equally among 30 students?

    <p>20</p> Signup and view all the answers

    What is the area of Mr. Dinesh's agricultural farm if the pond's area is 100 square meters?

    <p>400 square meters</p> Signup and view all the answers

    If a tank fills in 2 hours with both taps open, how long does it take for the smaller tap alone to fill the tank?

    <p>8 hours</p> Signup and view all the answers

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