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anemone
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Find all real solutions for the system \(\displaystyle 4x^2-40\left\lfloor{x}\right\rfloor+51=0\).
anemone said:Find all real solutions for the system \(\displaystyle 4x^2-40\left\lfloor{x}\right\rfloor+51=0\).
anemone said:Hi kaliprasad,
Nice try but the solutions aren't complete...:(
anemone said:Find all real solutions for the system \(\displaystyle 4x^2-40\left\lfloor{x}\right\rfloor+51=0\).
The quadratic formula is a mathematical formula used to solve quadratic equations. It is written as x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0. To solve the equation 4x^2-40x+51=0 using the quadratic formula, we would first identify the values of a, b, and c. In this case, a = 4, b = -40, and c = 51. Then, we would plug these values into the formula and solve for x. The resulting solutions are the roots of the equation.
Yes, this equation can be solved using factoring. To factor the equation 4x^2-40x+51=0, we would first look for common factors among the coefficients. In this case, all three coefficients are divisible by 1, so we can factor out a 1. Then, we would look for two numbers that multiply to give the constant term (51) and add up to give the coefficient of the middle term (-40). In this case, those numbers are -3 and -17. So, the equation can be factored as (x-3)(4x-17) = 0. This means that x = 3 or x = 17/4 are solutions to the equation.
Yes, it is possible for this equation to have complex solutions. Complex solutions occur when the discriminant (b^2 - 4ac) of the quadratic formula is negative. In this equation, the discriminant is (-40)^2 - 4(4)(51) = 1600 - 816 = 784, which is positive. Therefore, this equation does not have complex solutions.
No, this equation can have a maximum of two solutions. This is because it is a quadratic equation, which means it has the form ax^2 + bx + c = 0. A quadratic equation can have at most two solutions because it represents a parabola, which has two intersecting points with the x-axis. In the case of 4x^2-40x+51=0, we have already determined that there are two solutions, x = 3 and x = 17/4.
Yes, this equation can be solved without using the quadratic formula or factoring. One method is to graph the equation and find the x-intercepts, which represent the solutions to the equation. Another method is to use the method of completing the square, where we manipulate the equation to get it in the form (x + p)^2 = q. However, the most efficient and accurate method for solving this equation would be to use the quadratic formula or factoring.