Question

If the equation (3x)2 + (27 × 3 1/k – 15) x + 4 = 0 has equal roots, then k = (a) – 2 (b) -1/2 (c) 1/2 (d) 0 ​

Answer 1

k = -1/2

Step-by-step explanation:

The given equation is

9{x}^{2} + (27. {3}^{ \frac{1}{k} } - 15)x + 4 = 09x

2

+(27.3

k

1

−15)x+4=0

The quadratic equation has equal roots. Therefore the discriminant of the equation is zero.

d \: = {b}^{2} - 4ac \: = 0d=b

2

−4ac=0

{(27. {3}^{ \frac{1}{k} }-15) }^{2} - 4.9.4 = 0(27.3

k

1

−15)

2

−4.9.4=0

{(27. {3}^{ \frac{1}{k} } - 15)}^{2} = {12}^{2}(27.3

k

1

−15)

2

=12

2

27. {3}^{ \frac{1}{k}} - 15 = + - 1227.3

k

1

−15=+−12

27. {3}^{ \frac{1}{k} } = 27 \: or \: 327.3

k

1

=27or3

{3}^{ \frac{1}{k} } = 1 \: or \: \frac{1}{9}3

k

1

=1or

9

1

{3}^{ \frac{1}{k} } = {3}^{0} or \: {3}^{ - 2}3

k

1

=3

0

or3

−2

\frac{1}{k} = 0 \: or \: - 2

k

1

=0or−2

k \: = -\frac{1}{2}k=−

2

1

Since no finite k satisfy 1/k = 0, it is neglected.