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−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
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:
(x + 1 = 0 )
This simplifies to (x = -1).
(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=0 are:
(x = -1)
(x = 4)
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