Question

If α and β be the zeros of the quadratic polynomial 3x² +5x -7 Evaluate : 1/α + 1/β

Answer 1

${\huge{\underline{\sf {\orange{Answer}}}}}$

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$\frac{1 }{ \alpha } + \frac{1}{ \beta } = \frac{5}{7}$

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${\huge{\underline{\sf {\blue{Explanation :}}}}}$

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The polynomial is $3 {x}^{2} + 5x - 7$

The zeroes of this polynomial are α and β.

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The given polynomial is of the form

$a {x}^{2} + bx + c$

where, a = 3, b = 5, c = -7

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We know that,

Sum of zeroes = $\frac{ - b}{a}$

➣ $\alpha + \beta = \frac{ - b}{a}$

➣ $\alpha + \beta = \frac{ - 5}{3}$

Product of zeroes = $\frac{c}{a}$

➣ $\alpha \times \beta = \frac{c}{a}$

➣ $\alpha \times \beta = \frac{ - 7}{3}$

$\: \:$

Now,

We need to find,

$\frac{1}{ \alpha } + \frac{1}{ \beta }$

Taking LCM of α and β

$= \frac{ \beta \: + \: \alpha }{ \alpha \: \times \: \beta }$

$= \frac{ \alpha \: + \: \beta }{ \alpha \: \times \: \beta }$

$= \frac{ \frac{ - 5}{3} } { \frac{ - 7}{3} }$

$= \frac{ - 5}{3} \times \frac{3}{ - 7}$

$= \frac{ - 5}{ - 7}$

$= \frac{5}{7}$