Example 1: x^{2} + x  2 = 0
Example 2: 2x^{2} + √5x  5 = 0
Step 1: Comparing the given equation with
Answer: The roots are 1 and 2
ax^{2} + bx + c = 0
Step 2: Applying the Quadratic Formula, a = 1
 b = 1
 c = 2
Answer: The roots are 1 and 2
Example 2: 2x^{2} + √5x  5 = 0
Step 1: Compare the equation with,
Answer: Hence the roots are √5/2 and √5
ax^{2} + bx = c = 0
 a = 2
 b = √5
 c = 5
Answer: Hence the roots are √5/2 and √5
Example 3: 
Step 1: Convert the given quadratic equation
to standard form
Step 2: Compare the given equation with
to standard form
Multiplying throughout by 'x':  2x^{2}  1 = 7x 
Rewrite in standard form,  2x^{2}  7x  1 = 0 
ax^{2} + bx + c = 0
Step 3: Apply the Quadratic Formula a = 2
 b = 7
 c = 1
Answer:  Hence the roots are  and 
Example 4: 

Step 1: Convert the given quadratic equation
to standard form
Step 2: Compare the given equation with
Answer: Hence the roots are (3 + √6)
and (3  √6).
to standard form
By cross multiplication,  (x + 1)(2x + 3) = (3x + 2)(x + 3) 
By FOIL method,  2x^{2} + 5x + 3 = 3x^{2} + 11x + 6 
Simplify the equation,  (2x^{2} + 5x + 3)  (3x^{2} + 11x + 6) = 0 
x^{2}  6x  3 = 0  
Multiply throughout by 1,  x^{2} + 6x + 3 = 0 
ax^{2} + bx + c = 0
Step 3: Apply the Quadratic Formula a = 1
 b = 6
 c = 3
Answer: Hence the roots are (3 + √6)
and (3  √6).
Example 5:  √3x^{2} + 10x  8√3 
No comments:
Post a Comment