SOLVING TRINOMIALS WITH LEADING COEFFICIENT NOT EQUAL TO 1

Problem 1 :

4x² - 9 = 0

Solution:

4x² - 9 = 0

4x² = 9

x² = 9/4

x = ± 3/2

So, the solutions are {3/2, -3/2}. 

Problem 2 :

2x² + 4x + 1 = 0

Solution:

Comparing 2x² + 4x + 1 = 0 and ax² + bx + c = 0, we get

a = 2, b = 4 and c = 1

By using quadratic formula,

Problem 3 :

3x² - x - 1 = 0

Solution:

Comparing 3x² - x - 1 = 0 and ax² + bx + c = 0, we get

a = 3, b = -1 and c = -1

By using quadratic formula,

Problem 4 :

2x² - 5x + 1 = 0

Solution:

Comparing 2x² - 5x + 1 = 0 and ax² + bx + c = 0, we get

a = 2, b = -5 and c = 1

By using quadratic formula,

Problem 5 :

2x² + 6x + 4 = 0

Solution:

2x² + 6x + 4 = 0

2x² + 4x + 2x + 4 = 0

2x(x + 2) + 2(x + 2) = 0

(x + 2) (2x + 2) = 0

Equating each factor to 0, we get

x + 2 = 0 and 2x + 2 = 0

x = -1 or x = -2

So, the solutions are x = -1 or x = -2.

Problem 6 :

3x² + 15x + 18 = 0

Solution:

3x² + 15x + 18 = 0

3x² + 6x + 9x + 18 = 0

3x(x + 2) + 9(x + 2) = 0

(x + 2)(3x + 9) = 0

Equating each factor to zero, we get

x + 2 = 0 and 3x + 9 = 0

x = -2 and 3x = -9

x = -3

So, the solutions are x = -3 or x = -2.

Problem 7 :

2x² - 6x - 8 = 0

Solution:

2x² - 6x - 8 = 0

2(x² - 3x - 4) = 0

2(x² + x - 4x - 4) = 0

2(x(x + 1) - 4(x + 1)) = 0

2(x - 4) (x + 1) = 0

x - 4 = 0 or x + 1 = 0

x = 4 or x = -1

So, the solutions are x = 4 or x = -1.

Problem 8 :

x² = 6x + 27

Solution:

x² - 6x - 27 = 0

x2 - 9x + 3x - 27 = 0

x(x - 9) + 3(x - 9) = 0

(x + 3) (x - 9) = 0

x + 3 = 0 or x - 9 = 0

x = -3 or x = 9

So, the solutions are x = -3 or x = 9.

Problem 9 :

x² = 13x - 36 

Solution:

x² - 13x + 36 = 0

x² - 9x - 4x + 36 = 0

x(x - 9) - 4(x - 9) = 0

(x - 4) (x - 9) = 0

x - 4 = 0 or x - 9 = 0

x = 4 or x = 9

So, the solutions are x = 4 or x = 9.

Problem 10 :

2x² - 5x = 12

Solution:

2x² - 5x - 12 = 0

2x² + 3x - 8x - 12 = 0

x(2x + 3) - 4(2x + 3) = 0

(x - 4) (2x + 3) = 0

x - 4 = 0 or 2x + 3 = 0

x = 4 or 2x = -3

x = -3/2

So, the solutions are x = 4 or x =-3/2.

Problem 11 :

2 = 9x - 5x²

Solution:

5x² - 9x + 2 = 0

Comparing 5x² - 9x + 2 = 0 and ax² + bx + c = 0, we get

a = 5, b = -9 and c = 2

By using quadratic formula,