Q20 of 49 Page 1

For what value of k, the roots of the quadratic equation kx(x-2√5)+10 = 0 are equal?

The given Quadratic Equation is-


kx(x – 2√5) + 10 = 0


i.e. kx2-2√5kx+6 = 0


For Equal Roots, D should be equal to zero.


Discriminant D of the quadratic equation ax2+bx+c = 0 is given by-


D = b2 - 4ac


Comparing the equation ax2+bx+c = 0 with given quadratic equation kx2-2√5kx+6 = 0, we get-


a = k , b = –2√5k and, c = 10


∴ D = 0


⇒ (-2√5k)2-40k = 0


⇒ 20k2-40k = 0


⇒ 20k(k-2) = 0


⇒ k=0 or (k-2)=0


∴ k=0 or k=2


but k=0 is invalid, because then the given quadratic equation will become linear.


Hence, the required value of k is 2.


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