2y(2nd power)-11y+12
2007-12-20 09:27:52 · 5 answers · asked by ILIKETOPARTYY~! 3 in Science & Mathematics ➔ Mathematics
2y² - 11y + 12 = 0
The middle term is - 11y
Find the sum of the middle term
Multilply the first term 2 times the last term 12 equals 24 and factor.
Factors of 24
1 x 24
2 x 12
3 x 8. . .←. ,.Use these factors
4 x 6
- 8y and - 3y satisfy the sum of the middle term
insert - 8yand - 3y into the equation
2y² - 11y + 12 = 0
2y² - 8y - 3y + 12 = 0
Group factor
(2y² - 8y) - (3y + 12) = 0
2y(y - 4) -3(y - 4) = 0
(2y - 3)(y - 4) = 0
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Roots
2y - 3 = 0
Transpose 3
2y- 3 + 3 = 0 + 3
2y= 3
Divide both sides of the equation by 2
2y/ 2 = 3 / 2
y = 3/2
Insert the y value into the equation
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Roots
y - 4 = 0
Transpose 4
y = 4 + 4 = 0 + 4
y = 4
Insert the y value into the equation
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Check
y = 3/2
2x² - 11y + 12 = 0
2(3/2)² - 11(3/2) + 12 = 0
2(9/4) - 33/2 + 12 = 0
18/4 - 33/2 + 12 = 0
The common denomintor is 4
18/4 - 66/4 + 12 = 0
Subtract the numerator
- 48/4 + 12 = 0
Divide 4 into 48
- 12 + 12 = 0
0 = 0
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Check
y = 4
2y² - 11y + 12 = 0
2(4)² - 11(4) + 12 = 0
2(16) - 44 + 12 = 0
32 - 44 + 12 = 0
- 12 + 12 = 0
0 = 0
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The solution for Quadratic equation
2y² - 11y + 12 = 0
is
y = 3/2 and y = 4
- - - - - - - -s-
2007-12-20 09:57:14 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
factoring Ax^2 + Bx + C ==2y^2-11y+12
Step 1. Multiply together AC and list the factors of AC.
2*12=24
Step 2. Find a pair that adds (subtracts if C is neg) to B. If you cannot find such a pair then the trinomial does not factor.
1*24, 2*12, 3*8, 4*6 are the pairs...3+8=11 or C
Step 3. Rewrite the middle term as a sum of terms whose coefficients are the chosen pair.
2y^2-8y-3y+12
Step 4. Factor by grouping.
2y(y-4)-3(y-4)=(y-4)(2y-3)
2007-12-20 17:40:36 · answer #2 · answered by JAM 3 · 0⤊ 0⤋
trial and error!
write
2y^2 - 11y+12. factors of 2 are 1 and 2, factors of 12 are: 3,4; 6,2; 1, 12. Note 12 is positive, so they have the same sign, either both positive or both negative.
TRY:
(2y +4)(y +3 ), no
(2y -4)(y -3 ), no
(2y -3)(y -4 ), yes.
2007-12-20 17:31:19 · answer #3 · answered by pbb1001 5 · 0⤊ 0⤋
Simplifying
2y^2 + -11y + 12
Reorder the terms:
12 + -11y + 2y^2
Factor a trinomial.
(3 + -2y)(4 + -1y)
Final result:
(3 + -2y)(4 + -1y)
2007-12-20 17:40:35 · answer #4 · answered by Anonymous · 1⤊ 0⤋
(2y-3)(y-4) is your answer
2007-12-20 17:31:37 · answer #5 · answered by lfcwes 2 · 0⤊ 0⤋