Question

Find the discriminant of the following quadratic equation then state the number of rational, irrational, and imaginary solutions.
Equation: −6x2−6=−7x−9

Discriminant: Answer

Solutions:

Answer 1

Answer:

• -6x² - 6 = -7x - 9
• -6x² + 7x - 6 + 9 = 0
• -6x² + 7x + 3 = 0
• 6x² - 7x - 3 = 0

Discriminant:

• D = (-7)² - 4*6*(-3) = 49 + 72 = 121

Since D > 0, there are 2 real solutions:

• x = (- (-7) ±√121 )/12
• x = (7 ± 11)/12
• x = 1.5, x = -1/3

Answer 2

GIVEN:

• Equation:— – 6x² – 6 = – 7x – 9

ANSWER:

On simplifying equation, we get

• – 6x² + 7x – 6 + 9 = 0
• – 6x² + 7x + 3 = 0
• 6x² – 7x – 3 = 0

Discriminant(D) = b² – 4ac

• (–7)² – 4 × 6 × – 3
• 49 + 72
• 121

Since, D > 0 Then it has real solutions.

x = – b ± √D/2a

• –(–7) ± √121/2 × 6
• 7 ± 11/12
• 3/2 or –1/3.