Question

Write the value of the K for which the quadratic equation km(m - 2) + 6 = 0 has equal roots.

Answer 1

Answer:

Value of k is 6 .

Step-by-step explanation:

Given equation : km( m - 2 ) + 6 = 0

= >  km( m - 2 ) + 6 = 0

= >  km^2 - 2km + 6 = 0

Now, on comparing the formed equation with ax^2 + bx + c = 0, we get that a = k , b = - 2k , c = 6

We know that the discriminant of quadratic equation is b^2 - 4ac.

Now, substitute the value of a , b and c.

⇒ Discriminant = ( - 2k )^2 - 4( k x 6 )

⇒ Discriminant = 4k^2 - 24k

We know that the value of discriminant for equal roots is 0.

Now,

⇒ Discriminant = 0

= >  4k^2 - 24k = 0

= >  4k^2 = 24k

= >  4 k = 24

= >  k = 24 / 4

= >  k = 6

Therefore the numeric value of k is 6.

Answer 2

Lets go ....

Km(m - 2) +6

$= {km}^{2} - 2km + 6 \\ \\ a = k \\ b = - 2k \\ c = 6 \\ \\ we \: know \: {b}^{2} - 4ac = 0 \: for \: equal \: roots \\ \\ putting \: the \: value \: in \: formula \: we \: get \\ \\ = { (- 2k)}^{2} - 4 \times k \times 6 \\ \\ = {4k}^{2} - 24k \\ \\ = 4k(k - 6) \\ \\ 1st \: root \: \\ 4k = 0 \\ k = 0 \\ \\ 2nd \: root \: \\ k - 6 = 0 \\ k = 6 \\ \\ hence \: k \: is \: 6\: which \:will\:satisfy\:both\:the\:equation$