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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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Preeti Dabral 2 years, 10 months ago
Mrs. Bennet has been berating Mr. Bennet because he refused to go and visit with Mr. Bingley upon his arrival in the neighborhood (without Mr. Bennet introducing himself, the girls could not meet Mr. Bingley - thwarting Mrs. Bennet’s hopes of an advantageous marriage).
She continues to berate him the next day and Mr. Bennet plays along. He then casually mentions that he has already visited Mr. Bingley that morning. She then changes her tune, extolling his virtues to her children and telling them they have “an excellent father.” It is - as Jim mentioned - just a line to show how changeable and ridiculous she is.
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