find the root of 3x²-x-2=0
Answers
Answer:
Step by step solution :
STEP1:Equation at the end of step 1
(3x2 - x) - 2 = 0
STEP2: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
Equation at the end of step2:
(x - 1) • (3x + 2) = 0
Answer:
-2/3 or 1
Step-by-step explanation:
3x²-x-2=0
⇒3x²-3x+2x-2=0
⇒3x(x-1)+2(x-1)=0
⇒(x-1)(3x+2)=0
is, x-1=0 or,3x+2=0
∴x=1 ⇒3x=-2
∴x-2/3
∴x=1 or -2/3
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