Question

12. The equation x2 + 2x + 1 = (4 - kx)2 + 3 will be quadratic, if the value of k is: (a) k= 1 (b) k=1 (c) Any number (d) Insufficient data​

Answer 1

{Some corrections in the question}

The equation x² + 2x + 1 = (4 - kx)² + 3 will be quadratic, if the value of k is :

1. k = 1
2. k = 2
3. Any of the above
4. None of the above

Solution : Here, a/c to question;

Equation : x² + 2x + 1 = (4 - kx)² + 3

Now, we take k = 1

➜ x² + 2x + 1 = (4 - kx)² + 3

➜ x² + 2x + 1 = (4 - 1x)² + 3

➜ x² + 2x + 1 = 4² - 2*4*x + x² + 3

➜ x² + 2x + 1 = 16 - 8x + x² + 3

➜ x² + 2x + 1 = x² - 8x + 16 + 3

➜ x² + 2x + 1 = x² - 8x + 19

➜ x² - x² + 2x + 8x + 1 - 19 = 0

➜ 10x - 18 = 0

Compare above equation with ax² + bx + c = 0,

a = 0, b = 10 and c = - 18

The criteria for quadratic equation:

• The quadratic equation must equal zero; ax² + bx + c = 0.
• a must not equal zero. {a ≠ 0}

Therefore, the equation x² + 2x + 1 = (4 - kx)² + 3 will not be quadratic when the value of k is 2.

Now, we take k = 2

➜ x² + 2x + 1 = (4 - kx)² + 3

➜ x² + 2x + 1 = (4 - 2x)² + 3

➜ x² + 2x + 1 = 4² - 2*4*2x + (2x)² + 3

➜ x² + 2x + 1 = 16 - 16x + 4x² + 3

➜ x² + 2x + 1 = 4x² - 16x + 16 + 3

➜ x² + 2x + 1 = 4x² - 16x + 19

➜ x² - 4x² + 2x + 16x + 1 - 19 = 0

➜ - 3x² + 18x - 18 = 0

➜ 3x² - 18x + 18 = 0

Compare above equation with ax² + bx + c = 0,

a = 3, b = -18 and c = 18.

According to quadratic equation criteria;

Therefore, the equation x² + 2x + 1 = (4 - kx)² + 3 will be quadratic when the value of k is 2.

Answer : Therefore, the equation x² + 2x + 1 = (4 - kx)² + 3 will be quadratic when the value of k is 2.