Question

If 2 is a root of QE 3x²+qx-8=0 and the QE 4x²-2qx+k=0 has equal roots, find the value of k.​

Answer 1

Answer :

$\boxed{\bf k = 1}$

Step-by-step explanation:

   =>  2 is a root of QE 3x²+qx-8=0

 

   Put x = 2,

     3(2)² + q(2) - 8 = 0

      3(4) + 2q - 8 = 0

      12 + 2q - 8 = 0

       2q + 4 = 0

        2q = -4

        q = -4/2

        $\boxed{q=-2}$

    => the QE 4x²-2qx+k=0 has equal roots

   put q = -2,

    4x² - 2(-2)x + k =0

    4x² + 4x + k = 0

       It is of the form ax² + bx + c = 0

    a = 4, b = 4, c = k

For a quadratic equation having equal roots,

  Discriminant, D = b² - 4ac = 0

                 

          4² - 4(4)(k) = 0

          16 - 16k = 0

          16 = 16k

           k = 16/16

           k = 1