Question

find the value of k for the following quadratic equation so that they have two equal roots
x square- 2(5+2k)x+3(7+10k)=0​

please give the answer seriously this is my exam

Answer 1

Answer:

2 and 1/2

Step-by-step explanation:

The given equation x2 – 2(5 + 2k)x + 3(7 + 10k) = 0 is in the form of ax2 + bx + c = 0 Where a = 1, b = -2(5 + 2k), c = 3(7 + 10k) For the equation to have real and equal roots, the condition is D = b2 – 4ac = 0 ⇒ (-2(5 + 2k))2 – 4(1)( 3(7 + 10k)) = 0 ⇒ 4(5 + 2k)2 – 12(7 + 10k) = 0 ⇒ 25 + 4k2 + 20k – 21 – 30k = 0 ⇒ 4k2 – 10k + 4 = 0 ⇒ 2k2 – 5k + 2 = 0 [dividing by 2] Now, solving for k by factorization we have ⇒ 2k2 – 4k – k + 2 = 0 ⇒ 2k(k – 2) – 1(k – 2) = 0 ⇒ (k – 2)(2k – 1) = 0, k = 2 and k = 1/2 So, the value of k can either be 2 or 1/2

Answer 2

Step-by-step explanation:

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