Question

if the roots of the quadriatic equation xsquare+6x+k=0are equal then find the value of k

Answer 1

Answer:

quadratic equation ax^2+bx+c=0ax

2

+bx+c=0 has equal roots if

b^2-4ac=0b

2

−4ac=0 ...(1)

The given equation is

x^2+6x+k=0x

2

+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.

Step-by-step explanation:

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Answer 2

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${x}^{2} - 6x+k=0$

has discriminant

$D= {b}^{2} −4ac$

$=36−4k$

for real roots

$D>0$

$⇒ 36−4k>0$

$⇒ k<9$

The value of K is 9