Quadratic Equation Solver
ax2 + bx + c = 0
Input Coefficients
Solution
The two real roots are:
x1 = -2.0000
x2 = -3.0000
Steps to Solve
- The quadratic formula is: x = (-b ± √(b2 - 4ac)) / (2a)
- Substitute the values: a = 1, b = 5, c = 6 into the formula.
- This gives us: x = (-5 ± √(52 - 4(1)(6))) / (2(1))
- First, we solve the part under the square root, called the discriminant: Δ = b2 - 4ac = 52 - 4(1)(6) = 1.
- Since the discriminant is greater than 0, there are two distinct real solutions.
- x1 = (-5 + √1) / 2 = (-5 + 1.0000) / 2 = -2.0000
- x2 = (-5 - √1) / 2 = (-5 - 1.0000) / 2 = -3.0000
Educational Standards
This topic aligns with the following educational standards for secondary math education (grades 8-10):
Common Core State Standards (CCSS):
- HSA.REI.B.4.B: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Next Generation Science Standards (NGSS):
- MS-PS1-2: Analyze and interpret data on the properties of substances before and after they react to determine if a new substance was formed. (This is a cross-curricular connection, as quadratic equations can be used to model certain physical phenomena in chemistry and physics.)
- RST.6-8.3: Follow precisely a multi-step procedure when carrying out experiments, taking measurements, or performing technical tasks. (The process of using the quadratic formula is a multi-step procedure.)
