By factorization method 6y²-y-2=0
Answers
Answer:
Use the quadratic formula
=
−
±
2
−
4
√
2
y=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
y=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
6
2
−
−
2
=
0
6y^{2}-y-2=0
6y2−y−2=0
=
6
a={\color{#c92786}{6}}
a=6
=
−
1
b={\color{#e8710a}{-1}}
b=−1
=
−
2
c={\color{#129eaf}{-2}}
c=−2
=
−
(
−
1
)
±
(
−
1
)
2
−
4
⋅
6
(
−
2
)
√
2
⋅
6
y=\frac{-({\color{#e8710a}{-1}}) \pm \sqrt{({\color{#e8710a}{-1}})^{2}-4 \cdot {\color{#c92786}{6}}({\color{#129eaf}{-2}})}}{2 \cdot {\color{#c92786}{6}}}
y=2⋅6−(−1)±(−1)2−4⋅6(−2)
2
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Multiply the numbers
=
1
±
7
1
2
y=\frac{1 \pm 7}{12}
y=121±7
3
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
1
+
7
1
2
y=\frac{1+7}{12}
y=121+7
=
1
−
7
1
2
y=\frac{1-7}{12}
y=121−7
4
Solve
Rearrange and isolate the variable to find each solution
=
2
3
y=\frac{2}{3}
y=32
=
−
1
2
y=-\frac{1}{2}
y=−21
Solution
=
2
3
=
−
1
2
y=\frac{2}{3}\\y=-\frac{1}{2}
y=32y=−21
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Using factorization, find the roots of the quadratic equation: 6y2 - y
06-Jan-2018 — 6y2 - y - 2 = 0. 6y2 - 4y + 3y - 2 = 0. 2y (3y - 2) + (3y - 2) = 0. (2y + 1) (3y - 2) = 0. 2y + 1 = 0 3y - 2 = 0. y = -1/2 or y = 2/3.
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Answer:
y = 2/3 Or, -1/2
Step-by-step explanation:
6y² - y - 2 = 0
6y² - (4 - 3)y - 2 = 0
6y² - 4y + 3y - 2 = 0
2y(3y - 2) + 1(3y - 2) = 0
(3y - 2)(2y + 1) = 0
then,
3y - 2 = 0
3y = 2
y = 2/3
OR,
2y + 1 = 0
2y = -1
y = -1/2