Question

A student uses the quadratic formula to solve a quadratic equation and determines that one of the solutions is x equals negative seven plus square root of negative 245 end square root. What are the values of a and b if this solution is written in the form x = a + bi, where a and b are real numbers?"

Answer 1

The complex solution x = -7 + √(-245) can be written as x = -7 + 7i in the standard form a + bi, where a = -7 and b = 7.

Step-by-step explanation:

The student has used the quadratic formula to solve a quadratic equation and obtained a complex solution with a square root of a negative number. Since the square root of a negative number involves the imaginary unit i, where i is defined as the square root of -1, the student can express the complex number in the standard form a + bi, where a and b are real numbers. The given solution is x = -7 + √(-245). Firstly, we should simplify inside the square root: √(-245) = √(49×-5) = 7√i. Thus, the solution in the standard form is x = -7 + 7i, which implies that a = -7 and b = 7.