Question

find the discriminant. then state the number and type of solutions the quadratic equation would have based on this value. select the appropriate options from the drop-down menu provided.

\\-10n^2 = -13n + 4\\

the discriminant is select and the quadratic equation would have select solution(s).

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Write in standard form

Move all terms to one side to set the equation to zero:

$$ -10n^2 + 13n - 4 = 0 $$

Identify the coefficients:

$$ a = -10, \quad b = 13, \quad c = -4 $$

Step 2: Calculate the discriminant

Evaluate \( b^2 - 4ac \):

$$ (13)^2 - 4(-10)(-4) $$

$$ 169 - 160 = 9 $$

Step 3: Determine the number and type of solutions

Since the discriminant is positive (\( 9 > 0 \)) and a perfect square, the equation has:

• 2 real, rational solutions (or simply 2 real solutions depending on the dropdown options).

Answer:

• The discriminant is 9
• and the quadratic equation would have two real solution(s).