factorise the qudratic polynomial 3x^2-4x+2
Answers
Answer:
3x2-4x+2=0
Two solutions were found :
x =(4-√40)/-6=2/-3+1/3√ 10 = 0.387
x =(4+√40)/-6=2/-3-1/3√ 10 = -1.721
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((0 - 3x2) - 4x) + 2 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-3x2 - 4x + 2 = -1 • (3x2 + 4x - 2)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 + 4x - 2
The first term is, 3x2 its coefficient is 3 .
The middle term is, +4x its coefficient is 4 .
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 4 .
-6 + 1 = -5
-3 + 2 = -1
-2 + 3 = 1
-1 + 6 = 5
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = -3
B = -4
C = 2
Accordingly, B2 - 4AC =
16 - (-24) =
40
Applying the quadratic formula :
4 ± √ 40
x = —————
-6
Can √ 40 be simplified ?
Yes! The prime factorization of 40 is
2•2•2•5
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 40 = √ 2•2•2•5 =
± 2 • √ 10
√ 10 , rounded to 4 decimal digits, is 3.1623
So now we are looking at:
x = ( 4 ± 2 • 3.162 ) / -6
Two real solutions:
x =(4+√40)/-6=2/-3-1/3√ 10 = -1.721
or:
x =(4-√40)/-6=2/-3+1/3√ 10 = 0.387
Two solutions were found :
x =(4-√40)/-6=2/-3+1/3√ 10 = 0.387
x =(4+√40)/-6=2/-3-1/3√ 10 = -1.721