Question

find the discriminant.
\\(4w^2 + 9w = 0\\)
what type of solutions does the equation have?
one real solution
two real solutions
two complex (non - real) solutions

Explanation:

Step1: Recall the discriminant formula

For a quadratic equation \( ax^2 + bx + c = 0 \), the discriminant \( D \) is given by \( D = b^2 - 4ac \).
In the equation \( 4w^2 + 9w = 0 \), we have \( a = 4 \), \( b = 9 \), and \( c = 0 \).

Step2: Calculate the discriminant

Substitute the values of \( a \), \( b \), and \( c \) into the discriminant formula:
\( D = (9)^2 - 4(4)(0) \)
\( D = 81 - 0 \)
\( D = 81 \)

Step3: Determine the type of solutions

Since the discriminant \( D = 81>0 \), a quadratic equation with a positive discriminant has two distinct real solutions.

Answer:

The discriminant is \( 81 \), and the equation has two real solutions.