Question

5x2-4x+2+k(4x2-2x-1)=0 value of k which r the roots

Answer 1

B^2-4ac is the formula

Answer 2

Step-by-step explanation:

The given equation 5x2 – 4x + 2 + k(4x2 – 2x + 1) = 0

This can be rewritten as,

x2(5 + 4k) – x(4 + 2k) + 2 – k = 0

Now, this in the form of ax2 + bx + c = 0

Where a = (4k +5), b = -(2k + 4), c = 2 – k

For the equation to have real and equal roots, the condition is

D = b2 – 4ac = 0

⇒ (-(2k + 4))2 – 4(4k +5)(2 – k) = 0

⇒ (2k +4)2 – 4(4k +5)(2 – k) = 0

⇒ 16 + 4k2 + 16k – 4(10 – 5k + 8k – 4k2) = 0

⇒ 16 + 4k2 + 16k – 40 + 20k – 32k + 16k2 = 0

⇒ 20k2 + 4k – 24 = 0

⇒ 5k2 + k – 6 = 0

Now, solving for k by factorization we have

⇒ 5k2 + 6k – 5k – 6 = 0

⇒ 5k(k – 1) + 6(k – 1) = 0

⇒ (k – 1)(5k + 6) = 0,

k = 1 and k = -6/5,

So, the value of k can either be 1 or -6/5.

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