Algebra Class 10: Quadratic Equations
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Questions and Answers

What is the first step to simplify the equation $ rac{5}{x - 1} + rac{1}{4 - 3x} = rac{3}{6x - 8}$?

  • Set each fraction equal to zero.
  • Add all fractions together.
  • Substitute values for $x$.
  • Multiply each term by the common denominator. (correct)

    • If you multiply through by the common denominator, what will the equation look like?

  • $5(4 - 3x) + 1(x - 1) = 3$
  • $5(6x - 8) + 1(6x - 8) = 3(x - 1)$
  • $5(6x - 8) + 1(4 - 3x) = 3(x - 1)$
  • $5(6x - 8) + 1(x - 1) = 3(4 - 3x)$ (correct)

    • What is the simplified form of the equation after collecting like terms and moving all terms to one side?

  • $-2x^2 + 7x - 3 = 0$
  • $3x^2 - 5x + 8 = 0$
  • $x^2 - 2x + 4 = 0$
  • $2x^2 - 7x + 3 = 0$ (correct)

    • What method can be used to solve the quadratic equation $2x^2 - 7x + 3 = 0$?

    <p>Using the quadratic formula.</p> Signup and view all the answers

    What are the approximate solutions for $x$ after solving the equation $2x^2 - 7x + 3 = 0$?

    <p>$x = 2.5$ and $x = 0.5$</p> Signup and view all the answers

    Study Notes

    Simplifying the Equation

    • The first step to simplify the equation is to identify the common denominator of all the fractions involved.
    • The common denominator for the fractions (\frac{5}{x - 1}), (\frac{1}{4 - 3x}), and (\frac{3}{6x - 8}) is ((x - 1)(4 - 3x)).

    Multiplying Through by the Common Denominator

    • Multiplying each term of the equation by the common denominator eliminates the fractions.
    • After multiplying through, the equation becomes:
      • (5(4 - 3x) + 1(x - 1) = 3(x - 1))

    Collecting Like Terms and Rearranging

    • Simplifying the resulting equation involves distributing and combining like terms.
    • After rearranging all terms to one side, the simplified form is:
      • (2x^2 - 7x + 3 = 0)

    Solving the Quadratic Equation

    • To solve the quadratic equation (2x^2 - 7x + 3 = 0), methods such as factoring, completing the square, or using the quadratic formula can be employed.

    Approximate Solutions for (x)

    • Applying the quadratic formula yields approximate solutions (x \approx 3.5) and (x \approx 0.4285), which can be rounded as necessary.

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    Description

    Test your skills on solving the equation $ rac{5}{x - 1} + rac{1}{4 - 3x} = rac{3}{6x - 8}$. This quiz will guide you through the steps of simplifying the expression, moving terms, and solving the quadratic equation $2x^2 - 7x + 3 = 0$. Find the approximate solutions and enhance your understanding of algebraic concepts.

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