Math Question?

Question

Solve: (solving by grouping would be appreciated)

2x^3- 23x^2 +21x=0


Thanks

Answer 1

x(2x^2-23x+21)=0

x(x-1)(2x-21)=0

x=0, x=1, x=21/2

Answer 2

asking help for your homework huh. not good but try to pick up concepts from this.
2x^3- 23x^2 +21x=0

=>2 x(x^2-11.5x+10.5)=0---this step is intuitive--always try to make the term with highest power with a coefficient of 1, in this case x^2
=>2x(x-1)(x-10.5)=0--for this step, see the degree of x, biggest power is 2, that is the degree of this eqn(x^2-11.5x+10.5) so to split it you shld have two terms both having x like so. how to get the terms you have to figure out on your own, think of different ways of getting 10.5 by multiplying 2 numbers.. 3*3.5, 10.5 * 1. now which one will work -- -3-3.5 will give -6.5 but -10.5-1=-11.5 which is how u confirm the term..
=>2x(x-1)(x-10.5)=0
from this either x=0, or x=1, or x=10.5
if allowed use a calculator to find the 2 terms--its faster!!
the values for x are correct for d3m419s61 also but not for the others.
21/2 is 10.5
method gaurav_m used for arriving his answer is good for you if you can see that 2, the first coefficient and 21 the last add up to 23. Doesn't always happen:)

Answer 3

2x^3-23x^2+21x =0 IIIIII x( 2x^2 -23x +21) =0 ====> x=0 or
2x^2 -23x+21=0 IIIII x=(23+-19)/4
x= 21/2 x=1

Answer 4

2x³- 23x² +21x=0
x(2x² - 23x + 21) = 0
x = 0
d = -23² - 4.2.21
d = 529 - 168
d = 441

x = (23 +/- \/441) : 2.2
x' = (23 + 21) : 4
x' = 44 : 4 = 11
x" = (23 - 21) : 4
x" = 2 : 4 = 1/2
Solution: {x elements of R| x' = 11; x" = 1/2, x"' = 0}

Answer 5

x(2x^2-23x+21)=0
x(2x-21)(x-1)=0
x=0 x=21/2 x=1

Answer 6

2x^3-23x^2+21x=0
x(2x^2-23x+21)=0
x(2x^2-21x-2x+21)=0
x[x(2x-21)-1(2x-21)]=0
x[(x-1)(2x-21)]=0
x(x-1)(2x-21)=0

therefore x=0 or x=1 or x=21/2==11.5

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