The given function g(x) is a quadratic function of the form ax^2 + bx + c, where a, b, and c are all positive constants. Additionally, the discriminant D, which is calculated as b^2 - 4ac, is negative (D < 0).
When the discriminant is negative, it means that the quadratic equation does not have any real solutions. In other words, the quadratic function does not intersect the x-axis.
Since a, b, and c are all positive constants, this implies that the graph of g(x) opens upwards and does not intersect or cross the x-axis. As a result, the function g(x) is always positive (greater than zero) for every real value of x.
explain this
g(x) is of the form ax2+bx+c where a,b,c>0 and b2−4ac=D<0
Hence g(x)>0 for xϵR.
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1 answer