If α and β are the zeroes of the quadratic polynomial F (x) = x^2 + x − 2, find the value of
( 1/ α − 1 /β ).
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If α and β are the zeroes of the quadratic polynomial F (x) = x^2 + x − 2, find the value of
( 1/ α − 1 /β ).
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Solution:–
ㅤㅤF(x) = x² + x - 2
[ factorise the equation]
ㅤ✎ x² + 2x - 1x - 2
ㅤㅤ✎ x(x+2) -1(x+2)
ㅤㅤ ✎ (x-1) (x+2)
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ㅤㅤㅤx-1 = 0 | x+2 = 0
ㅤㅤㅤx = 1ㅤ | x = -2
[tex] {ㅤㅤ\mapsto\footnotesize\tt \alpha = 1 \: and \: \beta = - 2}[/tex]
[tex] {ㅤㅤ \implies\footnotesize\tt \ \frac{1}{ \alpha } - \frac{1}{ \beta } } \\ {ㅤㅤ \implies\footnotesize\tt \ \frac{1}{ 1 } - \frac{1}{ \ - 2 } } \\ {ㅤㅤ \implies\footnotesize\tt \ \frac{1}{ 1 } - ( \frac{ - 1}{ 2 } )} \\ { ㅤㅤ\implies\footnotesize\tt \ \frac{1}{ 1 } + \frac{1}{ 2 } } \\ {ㅤㅤ \implies\footnotesize\tt \ \frac{2 + 1}{ 2 }} \\ \\ { ㅤㅤ\implies\large\tt \ \frac{3}{ {2}}}[/tex]
[tex] \red{ㅤㅤㅤㅤ\underline\red{\boxed{ \frac{1}{ \alpha } + \frac{1}{ \beta}}}} \: = \huge\blue{\frac{3}{2}}[/tex]