Given eqN x^2 +k(4x+k-1) +2 =0 a=1 , b=4x+k-1, c= 2 formula:- sum of rOot =1/2 product of rOotaaga khud solve karO ;)exactly answer will be .....come value of "k"

Solution:

Let's analyze the given equation step by step.

Step 1: Expand the equation

The given equation is: x^k(4x^(k-1))^2 = 0

Simplifying the equation, we get: x^k * 16x^(2k-2) = 0

Step 2: Apply the zero product property

According to the zero product property, if a product of factors is equal to zero, then at least one of the factors must be zero.

In this case, the equation x^k * 16x^(2k-2) = 0 will have real and equal roots if either x^k = 0 or 16x^(2k-2) = 0.

Step 3: Solve for x^k = 0

Setting x^k = 0, we find that x = 0 (since any number raised to the power of 0 is equal to 1, except for 0^0 which is undefined).

Step 4: Solve for 16x^(2k-2) = 0

Setting 16x^(2k-2) = 0, we can divide both sides by 16 to get x^(2k-2) = 0.

Since we are looking for real and equal roots, we can ignore the possibility of complex numbers. Therefore, x^(2k-2) = 0 can only be true if x = 0.

Step 5: Combine the solutions

From Step 3, we found that x = 0 is a solution.

From Step 4, we found that x = 0 is also a solution.

Therefore, the only solution that satisfies the condition of having real and equal roots is x = 0.

Step 6: Determine the value of k

Since x = 0 is the only solution, we can substitute it back into the original equation to find the value of k.

Substituting x = 0 into the equation x^k(4x^(k-1))^2 = 0, we get 0^k(4*0^(k-1))^2 = 0.

Simplifying further, we have 0 * (0 * 0) = 0.

Since any number multiplied by 0 is equal to 0, we can conclude that the equation is true for any value of k.

Hence, the value of k can be any real number.

In summary, the equation x^k(4x^(k-1))^2 = 0 has real and equal roots for any value of k.