What is the best method to solve a quadratic equation with no "b"?
If a quadratic equation does not have a term with "b", it means that the coefficient of "b" is zero. In such cases, the quadratic equation is in the form of ax^2 + cx + d = 0.
To solve this type of quadratic equation, you can try to factor it or use the quadratic formula.
1. Factoring: If the quadratic equation can be factored, you can set it equal to zero and then factor it to find the values of x.
Example: x^2 + 6x + 9 = 0 can be factored as (x + 3)(x + 3) = 0. Therefore, x = -3.
2. Quadratic formula: If the quadratic equation cannot be easily factored, you can use the quadratic formula to find the values of x.
The quadratic formula is x = (-b ± √(b^2 - 4ac))/2a. However, since there is no "b" in this case, the formula simplifies to x = ± √(-4ac)/2a.
Example: 3x^2 - 12 = 0. The coefficient of "b" is zero, so using the quadratic formula gives x = ± √(-4(3)(-12))/2(3). Simplifying this gives x = ± √144/6 = ± √24 = ± 2√6.
So, in this case, the solutions are x = 2√6 and x = -2√6.