Factorise the quadratic expression $x^2 - x - 12$ - Junior Cycle Mathematics - Question 11 - 2013
Question 11
Factorise the quadratic expression $x^2 - x - 12$.
Use the factors from part (a) to solve the equation $x^2 - x - 12 = 0$.
Worked Solution & Example Answer:Factorise the quadratic expression $x^2 - x - 12$ - Junior Cycle Mathematics - Question 11 - 2013
Step 1
Factorise the quadratic expression $x^2 - x - 12$
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Answer
To factor the quadratic expression x2−x−12, we need to find two numbers that multiply to -12 (the constant term) and add to -1 (the coefficient of the middle term, x).
The numbers -4 and 3 satisfy these conditions since:
(−4)⋅(3)=−12
(−4)+(3)=−1
Thus, we can write the factorization as:
\(x + 3)(x - 4)\.
Step 2
Use the factors from part (a) to solve the equation $x^2 - x - 12 = 0$
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Answer
Using the factors from part (a):
[(x + 3)(x - 4) = 0]
We set each factor equal to zero:
x+3=0
Solving this gives: x=−3
x−4=0
Solving this gives: x=4
Therefore, the solutions to the equation x2−x−12=0 are:
x=−3 and x=4.
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