If one root of the quadratic equation 2×2 + kx + 1= 0 is -1/2 , then the value of k is​

2 thoughts on “If one root of the quadratic equation 2×2 + kx + 1= 0 is -1/2 , then the value of k is​”

1. Answer:

   –1

   Step-by-step explanation:

   The equation is: 2x² + kx + 1 = 0

   Let the another root be Ā.

   So, Ā×(–1/2)= 1/2

   =>Ā = 1/2×(–2/1)

   => Ā = –1

   Now, Ā + (1/2) = –k/2

   => –1+(1/2)=– k/2

   =>–1/2 = –k/2

   =>k = 1

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2. Answer:

   k=3 HOPE IT HELPS YOU

   Step-by-step explanation:

   We know

   addition of roots = -b/a

   multiplication of roots = c/a

   [tex]2x^2+kx + 1=0[/tex]

   a = 2

   b = k

   c = 1

   One root = -1/2

   Other root = ?

   Let other root = x

   addition of roots = -b/a

   -1/2 + x = -k/2

   x = -k/2 + 1/2 equation 1

   Now,

   Product of roots = c/a

   -1/2 * x = 1/2

   [tex]\frac{-1}{2} *x= \frac{1}{2} \\\\x = \frac{1*2}{2 * (-1)} \\x = 2/-2\\x = (-1)\\[/tex]

   Now putting value of x = (-1) in equation 1

   (-1) = -k/2 + 1/2

   (-1) – 1/2 = -k/2

   [tex]\frac{-2-1}{2} = \frac{-k}{2} \\\frac{-3}{2} = \frac{-k}{2} \\[/tex]

   -3 = -k

   k = 3

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