Question

if-2 is a root of the equation 3x + 7x+p=0, find
the value of k so that the roots of the equation
x²+k(4x+k- 1) +p=0 are equal.​

Answer 1

Answer:

There is a mistake in your question and it should be : If-2 is a root of the equation 3x² + 7x+p=0, find the value of k so that the roots of the equation x²+k(4x+k- 1) +p=0 are equal

Solution :

Given x = -2 is the root of equation 3x² + 7x + p = 0

Therefore, x = -2 satisfies the given equation.

3(-2)² + 7(-2) + p = 0

3(4) -14 + p = 0

12 - 14 + p = 0

-2 + p = 0

p = 2

So by putting the value of p in the given equation, we get

3x² + 7x + p = 0

3x² + 7x + 2 = 0

Now x² + k(4x + k - 1) + p = 0

Expanding the bracket, we get

x² + 4kx + k² - k + p = 0

Let's put up the value of p

x² + 4kx + k² - k + 2 = 0

The roots are equal.

Therefore, D = 0

b² - 4ac = 0

Comparing the equation with standard equation ax² + bx + c = 0, we get

a = 1, b = 4k and c = k² - k + 2

b² - 4ac = 0

(4k)² - 4 (1)(k² - k + 2) = 0

16k² - 4k² + 4k - 8 = 0

12k² + 4k - 8 = 0

4(3k² + k - 2) = 0

3k² + k - 2 = 0

3k² + 3k - 2k - 2 = 0

3k(k + 1) -2(k + 1) = 0

(3k - 2)(k + 1) = 0

3k - 2 = 0 ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀k + 1 = 0

3k = 2 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ k = -1

k = 2/3 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀k = -1

The values of k are 2/3 and -1

Answer 2

Answer:

The above answer is correct