Multiple Choice
Which mathematician is most commonly credited with developing the general solution for quadratic equations (often called the quadratic formula) in the 9th century?
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1. Equations & Inequalities
The Quadratic Formula
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Determine the number and type of solutions of the given quadratic equation. Do not solve.
A
2 real solutions
B
1 real solution
C
2 imaginary solutions
Verified step by step guidance1
Identify the standard form of a quadratic equation, which is ax^2 + bx + c = 0. In this case, the equation is -4x^2 + 4x + 5 = 0, where a = -4, b = 4, and c = 5.
To determine the number and type of solutions, calculate the discriminant using the formula: D = b^2 - 4ac.
Substitute the values of a, b, and c into the discriminant formula: D = (4)^2 - 4(-4)(5).
Simplify the expression to find the value of the discriminant.
Interpret the discriminant: If D > 0, there are 2 real solutions; if D = 0, there is 1 real solution; if D < 0, there are 2 imaginary solutions.
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