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विभक्त होने की क्रिया या भाव' या 'विभाग' या 'बाँट'। व्याकरण में शब्द (संज्ञा, सर्वनाम तथा विशेषण) के आगे लगा हुआ वह प्रत्यय या चिह्न विभक्ति कहलाता है जिससे पता लगता है कि उस शब्द का क्रियापद से क्या संबंध है।
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Preeti Dabral 2 years, 10 months ago (2983787)
Let {tex}\alpha{/tex} and 2{tex}\alpha{/tex} are the zeroes of the polynomial 2x2 - 5x - (2k + 1).
Then, 2{tex}\alpha{/tex}2 - 5{tex}\alpha{/tex} - (2k + 1) = 0
and 2 (2{tex}\alpha{/tex})2 - 5(2{tex}\alpha{/tex}) - (2k + 1) = 0
{tex}\Rightarrow{/tex} 2{tex}\alpha{/tex}2 - 5{tex}\alpha{/tex} = 2k + 1 ...(i)
and 8{tex}\alpha^2{/tex} - 10{tex}\alpha{/tex} = 2k + 1 ...(ii)
From Eqs. (i) and (ii), we get
2{tex}\alpha^2{/tex} - 5a = 8{tex}\alpha^2{/tex} - 10{tex}\alpha{/tex} {tex}\Rightarrow{/tex} 6{tex}\alpha^2{/tex} = 5{tex}\alpha{/tex} {tex}\Rightarrow{/tex} {tex}\alpha=\frac{5}{6}{/tex} {tex}[\because \alpha \neq 0]{/tex}
{tex}\therefore{/tex} 2{tex}\alpha{/tex} = {tex}\frac{5}{6} \times 2{/tex} {tex}=\frac{5}{3}{/tex}
Thus, the zeroes of the polynomial are {tex}\frac{5}{6}{/tex} and {tex} \frac{5}{3}{/tex}
Now, substituting {tex}\alpha=\frac{5}{6}{/tex} in Eq. (i), we get
2 {tex}\times{/tex} {tex} \frac{25}{36}-\frac{25}{6}{/tex} = 2k + 1
{tex}\Rightarrow{/tex} 2k + 1 = {tex}\frac{50-150}{36} {/tex} {tex}\Rightarrow 2 k+1{/tex} = {tex}-\frac{100}{36}{/tex}
{tex}\Rightarrow{/tex} 2k = {tex}-\frac{100}{36}-1{/tex} {tex} \Rightarrow{/tex} {tex} 2 k={/tex} {tex}-\frac{136}{36}{/tex}
{tex}\Rightarrow{/tex} k = - {tex}\frac{68}{36}{/tex} = {tex}\frac{-17}{9}{/tex}

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Sadaf Ashraf 2 years, 1 month ago (14994604)
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