What is the Value of (p+q-2t) and (p^2+q^2-2t^2) in an Equation with Degree 3?

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In summary, an equation with degree 3 has the highest exponent of 3 and is also known as a cubic equation. To solve it, one can use methods like factoring, the rational root theorem, or the cubic formula, and a graphing calculator can be helpful. This type of equation can have up to three real solutions or one real solution and two complex solutions, depending on the coefficients and constants. In real-world applications, equations with degree 3 are commonly used in physics, engineering, and economics to model various phenomena and solve optimization problems. There are also special techniques, such as substitution, elimination, and Gaussian elimination, that can be used to solve equations with degree 3.
  • #1
mahtaban
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I have an equation similar:
8x^3+4cx^2+2(b-3)x+(a-2c)=0
a, b, c are real number.
if p, q , t be roots.
What can say about (p+q-2t) and (p^2+ q^2-2t^2)?
Please help me??
Thanks so much.
 
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  • #2
hint: write your polynomial as 8(x-p)(x-q)(x-t) and multiply it out, then compare coefficients.
 
  • #3
I know
p+q+t=c/2
pq+pt+qt=(b-3)/4
pqt=(2c-a)/8
but I need value for
(p+q-2t)??
(p^2+ q^2-2t^2)?
Please help me??
 

FAQ: What is the Value of (p+q-2t) and (p^2+q^2-2t^2) in an Equation with Degree 3?

What does an equation with degree 3 mean?

An equation with degree 3 means that the highest exponent in the equation is 3. This is also known as a cubic equation.

How do you solve an equation with degree 3?

To solve an equation with degree 3, you can use methods such as factoring, the rational root theorem, or the cubic formula. It may also be helpful to use a graphing calculator to find approximate solutions.

3. Can an equation with degree 3 have multiple solutions?

Yes, an equation with degree 3 can have up to three real solutions or one real solution and two complex solutions. The number of solutions depends on the coefficients and constants in the equation.

4. What is the significance of an equation with degree 3 in real-world applications?

Equations with degree 3 are commonly used in physics, engineering, and economics to model real-world phenomena such as projectile motion, fluid flow, and supply and demand. They can also be used to solve optimization problems.

5. Are there any special techniques for solving equations with degree 3?

Yes, there are several techniques that can be used to solve equations with degree 3, such as the substitution method, the elimination method, and the Gaussian elimination method. It is important to choose the most efficient method based on the specific equation and its coefficients.

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