Posted by lizzie on Sunday, August 14, 2011 at 10:03am.
I don't know how to do this.
Which describes the number and type of roots of the equation x^3 - 4x^2 + 50x + 7 = 0?
a. 1 positive, 2 negative
b. 2 positive, 1 negative
c. 3 negative
d. 3 positive.
- algebra 2 - Anonymous, Sunday, August 14, 2011 at 10:54am
Let X1, X2, X3 are roots of the equation,
We can choose only b.
- algebra 2 - drwls, Sunday, August 14, 2011 at 10:58am
I don't know of any easy way to do this, so I used a website to provide a numerical solution.
None of the choic es are correct. Two of the roots are complex. The other is negative (-0.138414..)
Make sure you copied the problem correctly.
- algebra 2 - MathMate, Sunday, August 14, 2011 at 11:35am
There are two changes in the sign of the coefficients, so we have either 2 positive roots, or none.
Also, by negating the odd-powered terms, there is one change of sign, so we have 1 negative root. This invalidates choices a, c and d.
Without actually solving the equation, the choice is either
"none of the above", i.e. 2 complex and one negative root (as confirmed by drwls's solution).
Another way to see that there are 2 complex roots without solving the equation is to look at
which does not have real roots implying no maximum nor minimum. Therefore f(x) is monotonically increasing, and therefore has only one real root.
Answer this Question
More Related Questions
- Algebra II - Which describes the number and type of roots of the equation x^2 -...
- Algebra II - Find the exact solution to 6x^2+1= -8x by using the Quadratic ...
- Algebra 2/Trigonometry - How do I solve f(x)=x^3-6x^2+16x-96 using Descartes' ...
- algebra 1A - help please! the deepest point of the gulf of mexico lies ...
- math - describe the situation from the veiwpoint of each person. during a year a...
- Math - By drawing suitable sketches, state the number of (i) positive, (ii) ...
- Math - Which describes the number and type of roots of the equation x^2-625=0? A...
- Math - Could someone please explain to me how you get answers when you add a ...
- Algebra HELP! - Do not solve, show possibilities of Descartes's rule of signs ...
- Algebra - Do not solve, show possibilities of Descartes's rule of signs for ...