\(k\) āĻāϰ āĻā§āύ āĻŽāĻžāύ/ āĻŽāĻžāύāĻā§āϞāĻŋāϰ āĻāύā§āϝ \((3k+1)x^2+2(k+1)x+k=0\) āĻĻā§āĻŦāĻŋāĻāĻžāϤ āϏāĻŽā§āĻāϰāĻŖā§āϰ āĻŦāĻžāϏā§āϤāĻŦ āĻ āϏāĻŽāĻžāύ āĻŦā§āĻ āĻĨāĻžāĻāĻŦā§ āĻšāĻŋāϏāĻžāĻŦ āĻāϰ
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\((3k+1)x^2+2(k+1)x+k=0\)
āϏāĻŽā§āĻāϰāύāĻāĻŋāĻā§ \(ax^2+bx+c=0\) āϏāĻŽā§āĻāϰāĻŖā§āϰ
āϏāĻžāĻĨā§ āϤā§āϞāύāĻž āĻāϰ⧠āĻĒāĻžāĻ,
\( a=(3k+1),b=2(k+1)\) āĻāĻŦāĻ \(c=k \)
āϝā§āĻšā§āϤ⧠āĻŦā§āĻāĻĻā§āĻŦā§ āĻŦāĻžāϏā§āϤāĻŦ āĻ āϏāĻŽāĻžāύ,
â´āύāĻŋāϰā§āĻĒāĻ \(=0\)
āϏā§āϤāϰāĻžāĻ, \(b^2-4ac=0 \)
āĻ
āϰā§āĻĨāĻžā§, \({2(k+1) }^2-4Ã(3k+1)Ãk=0 \)
āĻŦāĻž, \(4(k^2+2k+1)-4(3k^2+k)=0 \)
āĻŦāĻž, \(k^2+2k+1-3k^2-k=0 \)
āĻŦāĻž, \(-2k^2+k+1=0 \)
āĻŦāĻž, \(2k^2-k-1=0 \)
āĻŦāĻž, \(2k^2-(2-1)k-1=0 \)
āĻŦāĻž, \(2k^2-2k+k-1=0 \)
āĻŦāĻž, \(2k(k-1)+1(k-1)=0 \)
āĻŦāĻž, \((k-1)(2k+1)=0 \)
\(â´k=1 \) āĻ
āĻĨāĻŦāĻž \(-\cfrac{1}{2}\)
\(â´k\) āĻāϰ āĻŽāĻžāύ \(1\) āĻ
āĻĨāĻŦāĻž \(-\cfrac{1}{2}\) āĻāϰ āĻāύā§āϝ āĻĒā§āϰāĻĻāϤā§āϤ āĻĻā§āĻŦāĻŋāĻāĻžāϤ
āϏāĻŽā§āĻāϰāĻŖā§āϰ āĻŦā§āĻāĻĻā§āĻŦā§ āĻŦāĻžāϏā§āϤāĻŦ āĻ āϏāĻŽāĻžāύ āĻšāĻŦā§ āĨ¤
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