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antiparticle
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If a(12a+5b+2c)>0 and the equation ax^2+bx+c=0 has roots y and z , then find out the range of the roots of the equation ...
antiparticle said:If a(12a+5b+2c)>0 and the equation ax^2+bx+c=0 has roots y and z , then find out the range of the roots of the equation ...
A quadratic equation is a mathematical expression in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It represents a parabola when graphed and has a degree of 2.
The roots of a quadratic equation can be found by using the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. This formula gives two possible values for x, known as the roots or solutions of the equation.
The range in a quadratic equation refers to the set of all possible values that the function can output. In other words, it is the set of all y-values that correspond to the x-values on the graph of the equation.
To determine the range of a quadratic equation, you can either graph the equation and observe the y-values, or you can use the vertex form of the equation, y = a(x-h)^2 + k, to find the minimum or maximum value of the function. The range will be all values of y that are equal to or greater than the minimum (if the parabola opens upwards) or equal to or less than the maximum (if the parabola opens downwards).
Yes, a quadratic equation can have no real roots if the discriminant (b^2 - 4ac) is negative. In this case, the solutions will be complex numbers (numbers with a real and imaginary part) instead of real numbers, and the parabola will not intersect the x-axis.