Question

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

\\-2x^2 - 6x - 7 = 0\\

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: Identify Coefficients

Identify the coefficients \(a\), \(b\), and \(c\) from the standard form quadratic equation \(ax^2 + bx + c = 0\):

$$ -2x^2 - 6x - 7 = 0 $$

$$ a = -2, \quad b = -6, \quad c = -7 $$

Step 2: Calculate the Discriminant

The discriminant formula is \(D = b^2 - 4ac\):

$$ D = (-6)^2 - 4(-2)(-7) $$

$$ D = 36 - 56 $$

$$ D = -20 $$

Step 3: Determine Number and Type of Solutions

Since the discriminant is negative (\(D < 0\)), the quadratic equation has no real solutions. Instead, it has two complex (imaginary) solutions.

Answer:

• The discriminant is \(-20\)
• and the quadratic equation would have two complex (or two imaginary / no real) solution(s).