Question

find the discriminant of the quadratic equation and give the number and type of solutions of the equation.\\(x^2 + 7x + 14 = 0\\)\
the discriminant is select \
so there is/ are select with options -7, 105, 21, 4

Explanation:

Step1: Recall discriminant formula

For a quadratic equation \(ax^2 + bx + c = 0\), the discriminant \(D\) is given by \(D = b^2 - 4ac\).
Here, \(a = 1\), \(b = 7\), \(c = 14\).

Step2: Calculate discriminant

Substitute the values into the formula:
\(D = 7^2 - 4\times1\times14\)
\(= 49 - 56\)
\(= -7\)

Answer:

The discriminant is \(-7\).

Now, for the number and type of solutions: Since the discriminant is negative (\(-7 < 0\)), there are 2 complex (non - real) solutions (specifically, two imaginary solutions that are complex conjugates of each other). But for the discriminant value from the given options, the answer is \(-7\).