Question

Find the values of k for each of the following quadratic equations, so that they have two
equal roots
$\: (1) \: \: 2{x}^{2} + kx + 3 \: = 0$
(2) kx (x - 2) +6=0​

Answer 1

Answer:

i)

If 2x

2

+kx+3=0 has equal roots, then b

2

−4ac=0.

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

x

2

+kx+3=0

b

2

−4ac=0

k

2

−4(2)(3)=0

k

2

=24

k=±

24

=±2

6

ii)

If kx

2

−2kx+6=0 has equal roots, then b

2

−4ac=0.

Here, a=k,b=−2k,c=6

kx(x−2)+6=0

kx

2

−2kx+6=0

4k

2

−4(k)(6)=0

4k

2

−24k=0

4k(k−6)=0

For k=0, equation is not quadratic.

k=6