find the roots using the formula x²-3x+2=0
Answers
Answer:
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Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
2
−
3
+
2
=
0
x^{2}-3x+2=0
x2−3x+2=0
=
1
a={\color{#c92786}{1}}
a=1
=
−
3
b={\color{#e8710a}{-3}}
b=−3
=
2
c={\color{#129eaf}{2}}
c=2
=
−
(
−
3
)
±
(
−
3
)
2
−
4
⋅
1
⋅
2
√
2
⋅
1
x=\frac{-({\color{#e8710a}{-3}}) \pm \sqrt{({\color{#e8710a}{-3}})^{2}-4 \cdot {\color{#c92786}{1}} \cdot {\color{#129eaf}{2}}}}{2 \cdot {\color{#c92786}{1}}}
x=2⋅1−(−3)±(−3)2−4⋅1⋅2
2
Simplify
Evaluate the exponent
Multiply the numbers
Subtract the numbers
Evaluate the square root
Multiply the numbers
=
3
±
1
2
x=\frac{3 \pm 1}{2}
x=23±1
3
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
3
+
1
2
x=\frac{3+1}{2}
x=23+1
=
3
−
1
2
x=\frac{3-1}{2}
x=23−1
4
Solve
Rearrange and isolate the variable to find each solution
=
2
x=2
x=2
=
1
x=1
x=1
Solution
=
2
=
1
answer is 1