Answer :

We know that if an equation *ax*^{2} + *bx* + *c* = 0 has two equal roots,

its discriminant

(*b*^{2} − 4*ac*) will be 0.

(i) 2*x*^{2} + *kx* + 3 = 0

Comparing equation with *ax*^{2} + *bx* + c = 0, we obtain,

*a* = 2, *b* = *k*, *c* = 3

Discriminate = *b*^{2} − 4*ac* = (*k*)^{2}− 4(2) (3) = *k*^{2} − 24

For equal roots,

Discriminant = 0

*k*^{2} − 24 = 0

*k*^{2} = 24

*=*

(ii) *kx* (*x* − 2) + 6 = 0

or *kx*^{2}− 2*kx* + 6 = 0

Comparing this equation with *ax*^{2} + *bx* + *c* = 0, we obtain,

*a* = *k*, *b* = −2 *k*, *c* = 6

Discriminant = *b*^{2} − 4*ac* = (− 2*k*)^{2} − 4 (*k*) (6) = 4*k*^{2} − 24*k*

For equal roots, *b*^{2} − 4*ac* = 0

*=* 4*k*^{2} − 24*k* = 0

= 4*k* (*k* − 6) = 0

Either 4*k* = 0 or *k* = 6

= *k* = 0 or *k* = 6

However, if *k* = 0, then the equation will not have the terms ‘*x*^{2}’ and ‘*x*’.

Therefore, if this equation has two equal roots, *k* should be 6 only.

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