8. If one factor of x² - 4x-12 is (x-6), then the other factor is?
Answers
Answer:
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Step-by-step explanation:
Determine what two numbers when added together make the coefficient of
x
, in this case
4
, and when multiplied together make the constant, in this case
−
12
. For this problem, the two numbers are
6
and
−
2
.
6
+
(
−
2
)
=
4
, and
6
×
(
−
2
)
=
12
.
The factorization of
x
2
+
4
x
−
12
=
(
x
−
2
)
(
x
+
6
)
.
Answer:
Question :-
\begin{gathered} {x}^{2} - 4x - 12 = 0 \\ \end{gathered}
x
2
−4x−12=0
What to find out =Roots of the equation?
Solution :-
Factorise by splitting middle term
\begin{gathered} {x}^{2} - 4x - 12 = 0 \\ \\ {x}^{2} - 6x + 2x - 12 = 0 \\ \\ x(x - 6) + 2(x - 6) = 0 \\ \\ (x - 6)(x + 2) = 0\end{gathered}
x
2
−4x−12=0
x
2
−6x+2x−12=0
x(x−6)+2(x−6)=0
(x−6)(x+2)=0
Now split it into possible cases
\begin{gathered}(x - 6) = 0 \\ \\ (x + 2) = 0\end{gathered}
(x−6)=0
(x+2)=0
Hence,
\begin{gathered}x_1 = (6) \\ \\ x_2 = ( - 2)\end{gathered}
x
1
=(6)
x
2
=(−2)