Solve for p, q, and r in 2x^2 − 12x + p = q(x − r)^2 + 10 for all x values

  • Thread starter DeanBH
  • Start date
In summary, the equation 2x^2 − 12x + p = q(x − r)^2 + 10 is true for all values of x. To find the values of p, q, and r, we can compare the corresponding coefficients of the squared terms on both sides of the equation. The correct values are q = 2, r = 3, and p = 28.
  • #1
DeanBH
82
0
2x^2 − 12x + p = q(x − r)^2 + 10 for all values of x find p q and r

i've got

2(x-3)^2 + p = Q(x-r)^2 + 10

so q = 2 r = 3 and p = 10?

now the answers say that Q = 2 r = 3 and p = 28?

can someone explain how to properly go about doing this equation.
 
Physics news on Phys.org
  • #2
2x^2 − 12x is not the same as 2(x-3)^2
 
  • #3
If a polynomial equation is true for all values of x, then "corresponding coefficients"- that is, coefficients multiplying the same powers of x on opposite sides of the equation- must be the same: multiply the square on the right and compare "corresponding coefficients".
 
  • #4
kamerling said:
2x^2 − 12x is not the same as 2(x-3)^2



k I've done it now, thx
 

1. How do I solve for the unknown values in an equation?

The first step is to identify what variable or variables you are trying to find. Then, use the given information and any known equations or rules to manipulate the equation until the unknown value(s) is isolated on one side. Finally, use algebraic techniques such as substitution or elimination to solve for the unknown value(s).

2. Can I use any method to solve an equation for unknown values?

No, it is important to use appropriate methods for solving equations. For simple linear equations, basic algebraic techniques such as addition, subtraction, multiplication, and division can be used. For more complex equations, it may be necessary to use more advanced techniques such as factoring, completing the square, or using the quadratic formula.

3. Can I solve an equation with multiple unknown values?

Yes, as long as there are enough equations and information given to solve for all the unknown values. This is known as a system of equations and can be solved using algebraic techniques such as substitution or elimination.

4. What should I do if I get a negative value as a solution for an unknown value?

If you are solving a real-world problem, it is important to check if the negative value makes sense in the context of the problem. If it does not, then the negative value is likely an extraneous solution and should be discarded. If you are solving a mathematical equation, then the negative value can be considered a valid solution.

5. How can I check if my solution for an unknown value is correct?

To check your solution, you can substitute the value back into the original equation and see if it satisfies the equation. If it does, then your solution is correct. Alternatively, you can also graph the equation and see if the point of intersection matches your solution.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
9
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
234
  • Precalculus Mathematics Homework Help
Replies
4
Views
2K
  • Precalculus Mathematics Homework Help
Replies
8
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
930
  • Precalculus Mathematics Homework Help
Replies
3
Views
2K
  • Math POTW for Secondary and High School Students
Replies
1
Views
714
  • Precalculus Mathematics Homework Help
Replies
2
Views
988
  • Precalculus Mathematics Homework Help
Replies
17
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
Back
Top