find the roots of the following. 3x2 -5x +2=0
Answers
Answer:
Step-by-step explanation:
3x2-x-2=0
Two solutions were found :
x = -2/3 = -0.667
x = 1
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(3x2 - x) - 2 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3x2-x-2
The first term is, 3x2 its coefficient is 3 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 3 • -2 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -1 .
-6 + 1 = -5
-3 + 2 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 2
3x2 - 3x + 2x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-1)
Add up the last 2 terms, pulling out common factors :
2 • (x-1)
Step-5 : Add up the four terms of step 4 :
(3x+2) • (x-1)
Which is the desired factorization
Answer:
x = 2/3 , 1
Step-by-step explanation:
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=^2 = -2/3 + (5/6)^2
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