2x^3 + x^2 - 5= 0
x=?
What is the process I must do in order to get the answer?
See your previous post
first guess
when does 2x^3 + x^2 = 5 ???
x | 2 x^3, x^2 , sum
o | 0 , 0 , 0
.5| .25 , .25 , .5
1 | 2 , 1 , 3
1.5| 6.75 , 2.25 , 9 yikes, try 1.25
1.25| 3.91 , 1.56 , 5.47 getting there
1.2 | 3.456 , 1.44 , 4.896
so between 1.2 and 1.25
1.22| 3.632 , 1.488 , 5.12
1.21| 3.543 , 1.464 , 5.007 close enough
so
x = 1.21 works
now you need 2 more roots
divide 2x^3 + x^2 - 5
by (x-1.21)
solve the resulting quadratic
Hey Fred, read previous answers before posting again.
To find the value of x that satisfies the equation 2x^3 + x^2 - 5 = 0, you can use the method called factoring or applying the rational root theorem. Let's go through the process step by step:
1. Start by rearranging the equation to bring all terms to one side, setting it equal to zero:
2x^3 + x^2 - 5 = 0
2. Try factoring out the equation. In this case, factoring directly may not be very straightforward, so we can use the rational root theorem to find potential rational solutions.
3. The rational root theorem states that if a rational number p/q is a root of the polynomial equation, then p is a factor of the constant term (-5 in this case), and q is a factor of the leading coefficient (2 in this case).
4. Find all the potential rational roots of the equation by forming fractions using combinations of factors of the constant term and the leading coefficient. In this case, the constant term (-5) factors to 1 and 5, while the leading coefficient (2) factors to 1 and 2:
Possible values for x: ±1/1, ±5/1, ±1/2, ±5/2
5. Substitute each potential rational root into the equation and check if it satisfies it. The ones that make the equation true are valid solutions.
6. Continue evaluating the potential roots until you find the roots of the equation. Alternatively, you may use methods such as long division or synthetic division to divide the polynomial equation by the factor (x - root), which will reduce the degree of the equation and allow you to solve it further.
Keep in mind that solving cubic equations can sometimes be challenging because it may not always have rational roots, and other methods like using the cubic formula or numerical approximation might be necessary.