Question

If α and β are the zeroes of the polynomial p(x)=x²+x-2.Find the value of 1/α-1/β[Don't spam and solve it quick please]

Answer 1

Answer is given in the attachment.

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Answer 2

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

If α and β are the zeroes of the polynomial p(x)=x²+x-2.Find the value of 1/α-1/β

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

★ Given that,

• α and β are the zeroes of the polynomial p(x) = x² + x - 2.

★ To find,

• Value of 1/α-1/β.

★ Let,

Factories the polynomial p(x) = x² + x - 2

$\rm:\implies x^{2} + x - 2 = 0$

$\rm:\implies x^{2} + 2x - x - 2 = 0$

$\rm:\implies x(x + 2) - 1(x + 2) = 0$

$\rm:\implies (x + 2)(x - 1) = 0$

$\rm:\implies x = - 2 \: or \: 1$

Hence, the zeroes are - 2 or 1.

Since, α = - 2 ; β = 1

★ Now,

$\rm:\implies \frac{1}{\alpha} - \frac{1}{\beta}$

$\rm:\implies -\frac{1}{2} - \frac{1}{1}$

$\rm:\implies \frac{-1-2}{2}$

$\rm:\implies \frac{-3}{2}$

$\underline{\boxed{\bf{\purple{ \therefore Hence,\:value\:of\:\frac{1}{\alpha} - \frac{1}{\beta} = \frac{-3}{2}}}}}\:\orange{\bigstar}$

★ More Information :

$\boxed{\begin{minipage}{7 cm} For a Quadratic Polynomial ax^{2} + bx + c = 0\\ \\ : \implies Sum\:of\:the\:zeroes : \alpha + \beta = -\frac{b}{a} \\ \\ :\implies Product\:of\:the\:zeroes:\alpha\beta= \frac{c}{a} \end{minipage}}$

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