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jeyben [28]
3 years ago
8

For what value of k are the roots of the quadratic equation kx (x-2)+6=0 equal?​

Mathematics
1 answer:
ser-zykov [4K]3 years ago
3 0

Answer:

\boxed{\sf k=6}

Step-by-step explanation:

\sf kx (x-2)+6=0

Expand brackets.

\sf kx^2 -2kx+6=0

This is in quadratic form.

\sf ax^2 +bx+c=0

Since this is for equal roots:

\sf b^2 -4ac=0

\sf a=k\\b=-2k\\c=6

\sf (-2k)^2 -4(k)(6)=0

\sf 4k^2-24k=0

\sf 4k(k-6)=0

\sf 4k=0\\k=0

\sf k-6=0\\k=6

Plug k as 0 to check.

\sf \sf 0x^2 -2(0)x+6=0\\6=0

False.

So that means k must equal 6.

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