Question

Find value of( α/β + β/α) for the quadratic polynomial

5x2

+ 4 – 7x

Pls reply fast
Wrong answers will be reported..... ​

Answer 1

$5 {x}^{2} + 4 - 7x = 0 \\ 5 {x}^{2} - 7x + 4 = 0 \\ \\ comaring \: \: \: with \\ \\ a {x}^{2} + bx + c = 0 \\ \\ a = 5 \: \: \: b = - 7 \: \: \: \: c = 4 \\ \\ \alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 7)}{5} = \frac{7}{5} \\ \\ \alpha \beta = \frac{c}{a} = \frac{4}{5} \\ \\ hence \\ \\ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ \\ = \frac{ {( \alpha + \beta ) }^{2} - 2 \alpha \beta }{ \alpha \beta } \\ \\ = \frac{ \frac{ {7}^{2} }{ {5}^{2} } - 2 \times \frac{4}{5} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{49}{25} - \frac{8}{5} \times \frac{5}{5} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{49}{25} - \frac{40}{25} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{49 - 40}{25} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{9}{25} }{ \frac{4}{5} } \\ \\ = \frac{9 \times 5}{25 \times 4} \\ \\ = \frac{9}{5 \times 4} \\ \\ = \frac{9}{20} \\ \\ hence \\ \\ \frac{ \alpha } { \beta } + \frac{ \beta }{ \alpha } = \frac{9}{20}$

Answer 2

Answer:

$\begin{gathered}5 {x}^{2} + 4 - 7x = 0 \\ 5 {x}^{2} - 7x + 4 = 0 \\ \\ comaring \: \: \: with \\ \\ a {x}^{2} + bx + c = 0 \\ \\ a = 5 \: \: \: b = - 7 \: \: \: \: c = 4 \\ \\ \alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 7)}{5} = \frac{7}{5} \\ \\ \alpha \beta = \frac{c}{a} = \frac{4}{5} \\ \\ hence \\ \\ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ \\ = \frac{ {( \alpha + \beta ) }^{2} - 2 \alpha \beta }{ \alpha \beta } \\ \\ = \frac{ \frac{ {7}^{2} }{ {5}^{2} } - 2 \times \frac{4}{5} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{49}{25} - \frac{8}{5} \times \frac{5}{5} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{49}{25} - \frac{40}{25} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{49 - 40}{25} }{ \frac{4}{5} } \\ \\ = \frac{ \frac{9}{25} }{ \frac{4}{5} } \\ \\ = \frac{9 \times 5}{25 \times 4} \\ \\ = \frac{9}{5 \times 4} \\ \\ = \frac{9}{20} \\ \\ hence \\ \\ \frac{ \alpha } { \beta } + \frac{ \beta }{ \alpha } = \frac{9}{20} \end{gathered}5x2+4−7x=05x2−7x+4=0comaringwithax2+bx+c=0a=5b=−7c=4α+β=a−b=5−(−7)=57αβ=ac=54henceβα+αβ=αβα2+β2=αβ(α+β)2−2αβ=545272−2×54=542549−58×55=542549−2540=542549−40=54259=25×49×5=5×49=209henceβα+αβ=209$