A family of functions is given:

f(x) = x^2 + 3x + k, where k is an element of {1, 2, 3, 4, 5, 6, 7}

One of these functions is chosen at random. Calculate the probability that the curve of this function crosses the x-axis.

Sub in the given values, 1 - 7 and see if the resulting quadratic has real solutions.

How many out of the 7 have real solutions and how many have complex solutions?

So I sub in the numbers each time for k, but what do I sub in for x?

You don't sub in anything for x, you solve the quadratic you get.

Could you please explain briefly how to solve quadratics?

first find the discriminant for all the values of k(D=b^2-4ac) but you will get a negative D on putting the third value so only first two values gives a positive D. so the curve of the equation will cut the x axis for first two values only, so now you can find the probability!

also here a is always positive so the parabola type(not exact parabola) graph of this given equation will always head upwards

Could you please explain briefly how to solve quadratics?

I am sorry to say, Imane, if you are that lost you need to see your instructor because this problem requires knowledge of quadratics. Either by solving them (which would be good practice) or by using the discrimant, as Rehann mentioned.

Rehann's suggestion of using the discrimant, b^{2}-4ac, would be the most quick.

If it is positive, then you have two real roots and it crosses the x-axis. If it is negative, then it has no real roots and does not cross the x-axis.

If it is 0, then it has one root of multiplicity 2 and just touches the x-axis without crossing it.