Questions: Compute the discriminant. Then determine the number and type of solutions of the given equation. 9x^2 - 2x + 5 = 0 What is the discriminant? - 176 (Simplify your answer.) Choose the sentence that describes the number and type of solutions of the quadratic equation. A. There are two imaginary solutions. B. There is one real solution. C. There are two unequal real solutions. D. There are an infinite number of real solutions.

Solution Steps

The quadratic equation is given as \( 9x^{2} - 2x + 5 = 0 \).
Here, the coefficients are:
\( a = 9 \), \( b = -2 \), and \( c = 5 \).

The discriminant \( D \) of a quadratic equation \( ax^{2} + bx + c = 0 \) is calculated using the formula:
\[ D = b^{2} - 4ac \]
Substitute the values of \( a \), \( b \), and \( c \):
\[ D = (-2)^{2} - 4(9)(5) \]
\[ D = 4 - 180 \]
\[ D = -176 \]

The discriminant \( D = -176 \) is negative.

• If \( D < 0 \), the quadratic equation has two imaginary solutions.
• Therefore, the correct choice is:
  A. There are two imaginary solutions.

Final Answer