Question
determine the # of real solutions 4x^2-2x=10
Answers
Answered by
GPT 3.5
To determine the number of real solutions of the equation 4x^2 - 2x = 10, we need to first rearrange the equation to make it easier to analyze.
4x^2 - 2x - 10 = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 4, b = -2, and c = -10.
The discriminant of a quadratic equation, given by D = b^2 - 4ac, helps determine the number of real solutions:
D = (-2)^2 - 4*4*(-10)
D = 4 + 160
D = 164
Since the discriminant D is positive (D > 0), the quadratic equation has two distinct real solutions.
4x^2 - 2x - 10 = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where a = 4, b = -2, and c = -10.
The discriminant of a quadratic equation, given by D = b^2 - 4ac, helps determine the number of real solutions:
D = (-2)^2 - 4*4*(-10)
D = 4 + 160
D = 164
Since the discriminant D is positive (D > 0), the quadratic equation has two distinct real solutions.