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Solve the equation $x^2 - 3x - 4 = 0.$ - Leaving Cert Mathematics - Question 5(a) - 2020

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Question 5(a)

Solve-the-equation-$x^2---3x---4-=-0.$-Leaving Cert Mathematics-Question 5(a)-2020.png

Solve the equation $x^2 - 3x - 4 = 0.$

Worked Solution & Example Answer:Solve the equation $x^2 - 3x - 4 = 0.$ - Leaving Cert Mathematics - Question 5(a) - 2020

Step 1

Step 1: Factor the Quadratic

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Answer

To factor the quadratic equation x2−3x−4x^2 - 3x - 4, we need to find two numbers that multiply to (-4) (the constant term) and add to (-3) (the coefficient of the linear term). These numbers are (+1) and (-4). Thus, we can rewrite the equation as:

(x+1)(x−4)=0(x + 1)(x - 4) = 0

Step 2

Step 2: Set Each Factor to Zero

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Answer

Setting each factor equal to zero gives us the possible values for x:

  1. (x + 1 = 0 )
    This simplifies to (x = -1).
  2. (x - 4 = 0 )
    This simplifies to (x = 4).

Step 3

Step 3: State the Solutions

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Answer

Thus, the solutions to the equation x2−3x−4=0x^2 - 3x - 4 = 0 are:

  • (x = -1)
  • (x = 4)

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