Question

If the roots of x2 +6Kx + K = 0 are equal, the value of K is​

Answer 1

Question:-

If the roots of x² +6Kx + K = 0 are equal, the value of K is ___.

Answer:-

If roots of a polynomial are equal then

D = 0

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

here

b = 6k, a = 1 and c = k

So,

→(6k)² - 4.1.k = 0

→36 k² - 4k = 0

→4k ( 9k - 1 ) = 0

So →4k = 0 and →9k - 1 = 0

→k = 0 and→ k = 1/9 ( ans).

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Answer 2

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➡️A quadratic equation x²+bx+c=0ax²+bx+c=0 has equal roots if

b²-4ac=0b²−4ac=0            

The given equation is

x²+6x+k=0x2+6x+k=0

Here, a=1, b=6 and c=k. Substitute these values in equation (1).

(6)²-4(1)(k)=0(6)2−4(1)(k)=0

36-4k=036−4k=0

Subtract 36 from both sides.

-4k=-36−4k=−36

Divide both sides by -4.

k=9k=9

Therefore, the value of k is 9.