solve
by
formala methed: 3x²-5x+7=0
Answers
The roots (answers) are:
x
=
5
+
i
√
59
6
and,
x
=
5
−
i
√
59
6
Hence there are no real roots to this quadratic, which means it does not cross the x-axis.
Explanation:
3
x
2
−
5
x
+
7
=
0
is a quadratic equation. This can be solved in 3 ways: factorising, using the quadratic formula or by completing the square. It's not obvious how to factorise
3
x
2
−
5
x
+
7
=
0
so we'll use the quadratic formula:
x
=
−
b
±
√
b
2
−
4
a
c
2
a
a is the coefficient of
x
2
, in this case 3.
b is the coefficient of
x
, in this case -5.
c is the constant, in this case 7.
Putting these values into the quadratic equation:
x
=
−
(
−
5
)
±
√
(
−
5
)
2
−
4
(
3
)
(
7
)
2
(
3
)
x
=
5
±
√
25
−
84
6
x
=
5
±
√
−
59
6
x
=
5
±
i
√
59
6
So the roots are:
x
=
5
+
i
√
59
6
and,
x
=
5
−
i
√
59
6
√
−
59
is an imaginary number, equal to
√
−
1
√
59
, which equals
i
√
59
. The symbol for the square root of -1 is i. Thus the roots of this equation have a real part (the 5/6) and an imaginary part (the
±
i
√
59
6
). A number made up of a real and imaginary part is called a complex number. Hence there are no real roots to this quadratic, which means it does not cross the x-axis.
Answer:
x= 5+√−59 or x= 5-√−59
6 6
Step-by-step explanation:
Formula Name:
Factorisation formula.
3x²-5x+7=0
Let's solve your equation step-by-step.
3x²−5x+7=0
For this equation: a=3, b=-5, c=7
3x²+−5x+7=0
Step 1: Use quadratic formula with a=3, b=-5, c=7.
x= −b±√b2−4ac
2a
Putting in values
x= −(−5)±√(−5)2−4(3)(7)
2(3)
x= 5±√−59
6
x= 5+√−59 or x= 5-√−59
6 6