Can anyone please teach me how to solve for x in terms of a,b,c in this problem?
Thanks a lot!
ax^2+bx+c=0
Well, the general approach to solving equations of this kind is by using something known as a determinant.
The determinant of this equation is found by the following formula:
D=b²-4ac
(this formula is found by using Horners theorems on second degree equations, but I won't be going into depth on this subject)
There are 3 possible scenario's:
1)The determinant is negative (D<0): in this case there are no solutions for the problem.
2)The determinant is 0 (D=0): in this case there are two solutions, but both solutions have the same answer, so we only find 1 unique value as a solution
3)The determinant is positive (D>0): in this case there are two different solutions.
In cases 2 and 3, the two solutions can be calculated by using the equations:
x1 = (-b+sqrt(D))/(2a)
x2 = (-b-sqrt(D))/(2a)
We have now found the two possible solutions for the equation.
P.S. This is the most general approach for solving a second degree equation. Depending on the situation, there are possibly easier ways for solving, but you have to find that out for yourself.
Slove 4a=a+2d and -8=a+8d using substitution method
Certainly! To solve for x in terms of a, b, and c in the given quadratic equation ax^2 + bx + c = 0, we can use the quadratic formula. The quadratic formula states that for any quadratic equation in the form of ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
To apply the quadratic formula to the given equation:
1. Identify the values of a, b, and c from the equation ax^2 + bx + c = 0.
2. Substitute these values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
3. Simplify the equation and compute the square root if necessary.
4. Apply the "plus-minus" symbol (±) to account for both possible solutions.
Let's walk through an example to illustrate the process:
Example:
Given the equation 3x^2 + 5x - 2 = 0, we can solve for x:
1. Identify the values of a, b, and c:
- a = 3
- b = 5
- c = -2
2. Substitute the values into the quadratic formula:
x = (-5 ± √(5^2 - 4 * 3 * -2)) / (2 * 3)
3. Simplify the equation:
x = (-5 ± √(25 + 24)) / 6
x = (-5 ± √49) / 6
x = (-5 ± 7) / 6
4. Apply the "plus-minus" symbol (±):
x = (-5 + 7) / 6 or x = (-5 - 7) / 6
x = 2 / 6 or x = -12 / 6
x = 1/3 or x = -2
Therefore, the solutions for x in terms of a, b, and c in the equation 3x^2 + 5x - 2 = 0 are x = 1/3 and x = -2.
Remember to always double-check your work and simplify the solutions if needed.