Question

what is the value(s) of p for which the quadratic equation 4x^2- 2(k +1)x +(k+1) =0 has equal roots?​

Answer 1

Answer:

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Answer 2

The correct answer is "k = 3" and "k = -1". Further explanation is given below.

Step-by-step explanation:

Given equation is:

4x²-2(k+1)x+(k+1) = 0

If it has equal roots, then

As we know,

b²-4ac = 0

On putting the values, we get

⇒  (-2(k+1))²-4(4)(k+1) = 0

⇒  4(k+1)²-16k-16 = 0

⇒  4(k²+1+2k)-16k-16 = 0

⇒  4k²+4+8k-16k-16 = 0

⇒  4k²-8k-12= 0

On taking "4" as a common, we get

⇒  4(k²-2k-3)= 0

⇒  k²-2k-3 = 0

⇒  k²-3k+k-3 = 0

⇒  k(k-3)+1(k-3) = 0

⇒  (k+1) (k-3) = 0

⇒  k+1 = 0

⇒ k = -1

Or,

⇒  k-3 = 0

⇒ k = 3

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