## Pages

### Additional solved examples for Quadratic Formula

Example 1:    x2 + x - 2 = 0

Step 1: Comparing the given equation with

ax2 + bx + c = 0

• a = 1
• b = 1
• c = -2
Step 2: Applying the Quadratic Formula,

 Positive root Negative root:

Answer: The roots are 1 and -2

Example 2: 2x2 + √5x - 5 = 0

Step 1: Compare the equation with,

ax2 + bx = c = 0
• a = 2
• b = √5
• c = -5
Step 2: Applying the Quadratic Formula,

 (Positive root) (Negative root)
Answer: Hence the roots are √5/2 and -√5

 Example 3:

Step 1: Convert the given quadratic equation
to standard form

 Multiplying throughout by 'x': 2x2 - 1 = 7x Rewrite in standard form, 2x2 - 7x - 1 = 0
Step 2: Compare the given equation with

ax2 + bx + c = 0

• a = 2
• b = -7
• c = -1
Step 3: Apply the Quadratic Formula

 (Positive root) (Negative root)

 Answer: Hence the roots are and

Example 4:
 (x + 1)/(x + 3) = (3x + 2)/(2x + 3)

Step 1: Convert the given quadratic equation
to standard form

 By cross multiplication, (x + 1)(2x + 3) = (3x + 2)(x + 3) By FOIL method, 2x2 + 5x + 3 = 3x2 + 11x + 6 Simplify the equation, (2x2 + 5x + 3) - (3x2 + 11x + 6) = 0 -x2 - 6x - 3 = 0 Multiply throughout by -1, x2 + 6x + 3 = 0
Step 2: Compare the given equation with

ax2 + bx + c = 0

• a = 1
• b = 6
• c = 3
Step 3: Apply the Quadratic Formula

 x = -3 +/- √6 Positive root: x = -3 + √6 Negative root: x = -3 - √6

Answer: Hence the roots are (-3 + √6)
and (-3 - √6).

 Example 5: √3x2 + 10x - 8√3
Step 1: Compare the given equation with

ax2 + bx + c = 0

• a = √3
• b = 10
• c = -8√3
Step 2: Apply the Quadratic Formula

 (Positive root) (Negative root)

 Answer: Hence the two roots are (after ratinalizing) (2√3)/3 and -4√3