Find the real solutions of this equation. 3x3 + 4x2 - 7x + 2 = 0?

Question

Find the real solutions of this equation.
3x3 + 4x2 - 7x + 2 = 0
Please Show Work!!!!!!
Thanks!

Answer 1

f(-3) = -21 and f(0) = 2) Thus there is a root between -3 and 0. It looks like the root will be closer to -3 than to 0. So take another guess of say -2. f(-2) = 8, so root lies between -3 and
-2. Now you need to use Newton's method to zero in on the value of the root to whatever degree of accuracy you want.

Then you need to repeat the process to find the other roots. You will find they lie betwwen .4 and .41 and between .65 and .67

Answer 2

If this is the third degree polynomial 3x³ + 4x² - 7x + 2 = 0...

3x³ + 4x² - 7x + 2 = 0
3x³ + 4x² + [(2x² + 3x) - (2x² + 3x)] - 7x + 2 = 0
(3x³ + 4x² + 2x² + 3x) + (-2x² - 3x - 7x + 2) = 0
(3x³ + 6x² + 3x) + (-2x² -10x + 2) = 0
3x(x² + 2x + 1) + (-2)(x² + 5x - 1) = 0
3x(x + 1)² + (-2)[x² + (2x + 3x) + (1 -1) – 1] = 0
3x(x + 1)² + (-2)[(x² + 2x + 1) + 3x - 2] = 0
3x(x + 1)² + (-2)[(x + 1)² + 3x - 2] = 0
3x(x + 1)² + (-2)[(x + 1)²] + (-2)(3x – 2) = 0
(3x – 2)(x + 1)² + (-2)(3x – 2) = 0
(3x – 2)[(x + 1)² -2] = 0

Thus, the roots can be found from:

0 = 3x - 2
⅔ = x

0 = (x + 1)² - 2
√2 = √(x + 1)²
√2 = |x + 1|
√2 = ±(x + 1)
√2 = x + 1 or √2 = -x - 1
√2 -1 = x or x = -1 - √2

Answer 3

In general I make it a practice not to do people's homework for them. But here are the tools you need to solve that.

First, make it as simple as you can. Some of the math you can do along the way. For instance, I'm not spilling too many beans if I say to replace 3x3 with 9. Right?

Second, it is always true that if you have an equation, you can perform the same operation to both sides of the equation, and the result is still an equation. If two things are equal and you add 11 to both sides, they are still equal. If two things are equal and you take half of each, then the remaining halves are still equal. Makes sense, right?

Third, just so you don't cross yourself up, remember precedence. If you don't have parentheses or something to make it clear for you, you multiply and/or divide before you add and/or subtract. So if someone asks you to solve 4 + 3 x 2, the answer is 10, because you do 4 + (3 x 2). In particular, the answer is NOT 14, because you do not do (4 + 3) x 2.

So with those three things in mind. Simplify the problem, doing all the easy math, keeping in mind the rules of precedence. Eventually you'll find yourself with a much simpler equation that has a pesky 'x' in it. Do whatever you need to do to both sides of equation so that only the 'x' is left on one side. What is left on the other side is your answer. An example of a problem that requires similar skills:

2 + 3 x 4 + 1/2 n = 36
Do the easy math stuff, getting the precedence right:
24 + 1/2 n = 36
That's better, but not good enough. What if I subtract 24 from both sides of the equation?
1/2n = 12
So close. But I need to end up with just n on the left hand side. I know - multiply both sides of the equation by 2:
2 * 1/2n = 2 * 12
1n = 24
n=24

Hope that helps...

Answer 4

First combine like terms

3x3 + 4x2 - 7x + 2 = 0?
4x2 3
-7x 2 0x7=0 answer

Answer 5

i couldnt find a solution for that problem

3x3=9
4x2=8

9+8=17

7x2=14

17-14+2=5 not the answer

7x3=21

17-21+2= -2 not the answer.

I couldnt find one, so no solution