Problema Solution

in the xy-plane, the graph of the function f(x) = x2 + bx + 4 does not intersect the x-axis. what is the value of b?

Answer provided by our tutors

the graph of the function f(x) = x^2 + bx + 4 does not intersect the x-axis when the quadratic equation


x^2 + bx + 4 = 0 has no real roots


the happens when the discriminant of the equation is < 0


discriminant = b^2 - 4*4*1


b^2 - 4*4*1 < 0


b^2 - 16 < 0


b^2 < 16


|b| < 4^2


|b| < 4


-4 < b < 4


for example for b = 1 we have f(x) = x^2 + x + 4 and we draw the graph we will see that is doesn't intersect the x-axis


click here to see the graph of f(x) = x^2 + x + 4


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