Question

find the value of k for eqn x2 +5kx+16=0 has roots and equal roots

Answer 1

Answer:

Numeric value of k is 8 / 5 or - 8 / 5 .

Step-by-step explanation:

Given equation : x^2 + 5kx + 16 = 0

On comparing the given equation with ax^2 + bx + c = 0, we get

a = 1 , b = 5k , c = 16

Discriminant = b^2 - 4ac

We know, when the equation contains real and equal roots, value of discriminant becomes 0.

So,

b^2 - 4ac = 0

Now,

= >  b^2 - 4ac = 0

= >  ( 5k )^2 - 4( 1 x 16 ) = 0

= >  25k^2 - 64 = 0

= >  25k^2 = 64

= >  k^2 = 64 / 25

= >  k^2 = ( 8 /  5 )^2  or  ( - 8 / 5 )^2

= >  k = 8 / 5  or  - 8 / 5

Therefore the value of k is 8 / 5  or  - 8 / 5 .

Answer 2

we have,
a=1,b=5k and c =16
it is given that roots are equal
i.e. d = b2-4ac
d= (5k)2-4(1)(16)
25k2-64. (-4*16=-64)
25k2= +64
k2=64/25
k=root 64/25
k=8/5 (ans.) (root of 64 is 8 while root of 25 is 5)