find the zeroes of the polynomial 49x^2-64
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Step-by-step explanation:
We know that, 49 is the square of 7 and 64 is the square of 8. To find the zeroes, we have to use zero product rule. Hence, the zeroes are - 8/7 and 8/7.
49
x
2
−
64
=
0
or
(
7
x
)
2
−
(
8
)
2
=
0
or
(
7
x
+
8
)
(
7
x
−
8
)
=
0
∴
(
7
x
−
8
)
=
0
or
(
7
x
+
8
)
=
0
∴
x
=
8
7
or
x
=
−
8
7
Usually we make a quadratic equal to 0 to be able to solve it.
This is an exception, where we can use the normal method of x on one side and the numbers on the other.
49
x
2
=
64
x
2
=
64
49
find the square root of both sides
x
=
±
√
64
49
x
=
=
8
7
or
x
=
−
8
7
However, we can also use the factorising method:
49
x
2
−
64
=
0
the difference of two squares
(
7
x
+
8
)
(
7
x
−
8
)
=
0
x
=
−
8
7
or
x
=
8
7
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