Question

if a and b are zeros of the polynomial 4x^3+3x+7 then find the value of 1/a+1/b​

Answer 1

I think it's x^2

then the answer is..

-3/7

Answer 2

☯ Given that, $\sf \alpha$ and $\sf \beta$ are zeros of the polynomial $\sf 4x^3 + 3x + 7$.

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☯ We have to find value of $\sf \dfrac{1}{ \alpha } + \dfrac{1}{ \beta }$

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★ Given quadratic equation = $\bf 4x^3 + 3x + 7$

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$\star\;{\frak{Here}} \begin{cases} & \text{a = 4} \\ & \text{b = 3 } \\ & \text{c = 7}\end{cases}$

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

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${\underline{\sf{\bigstar\;Sum\;of\;zeros\;( \alpha + \beta ) = \bf{{}^{\text {-b}}\!/{}_{\text{a}}}}}}$

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$:\implies\bf ( \alpha + \beta ) = \dfrac{-3}{4}$

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$\dag\;{\underline{\frak{Also,\;We\;know\;that,}}}$

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${\underline{\sf{\bigstar\; Product\;of\;zeros\;( \alpha \beta ) = \bf{{}^{\text {c}}\!/{}_{\text{a}}}}}}$

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$:\implies\bf ( \alpha \beta ) = \dfrac{7}{4}$

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Now,

${\underline{\sf{\bigstar\;Using\; Identity\;of\; quadratic\; expression,}}}$

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$\star\;{\boxed{\sf{\pink{\dfrac{1}{ \alpha} + \dfrac{1}{ \beta}}}}}$

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$:\implies\sf \dfrac{ \alpha + \beta}{ \alpha \beta}$

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$\dag\;{\underline{\frak{Putting\;values,}}}$

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$:\implies\sf \dfrac{ \dfrac{-3}{4}}{ \dfrac{7}{4}}$

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$:\implies\sf \dfrac{ \dfrac{-3}{ \cancel{4}}}{ \dfrac{7}{ \cancel{4}}}$

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$:\implies\sf{\underline{\boxed{\sf{\pink{ \dfrac{-3}{7}}}}}}\;\bigstar$

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$\therefore$ value of $\sf \dfrac{1}{ \alpha } + \dfrac{1}{ \beta }$ is $\bf \dfrac{-3}{7}$.

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$\star\;{\underline{\underline{\sf{\purple{Polynomial\;:}}}}}$

• An expression having more than two algebraic terms.

• It consist of variables, coefficients and exponents.

• Polynomial is made up of two terms, namely Poly means "many" and Nominal means "terms".

• Polynomial containing degree 0 is know as Constant or Zero Polynomial.
• Polynomial containing degree 1 is know as Linear Polynomial.
• Polynomial containing degree 2 is know as Quadratic Polynomial.
• Polynomial containing degree 3 is know as Cubic Polynomial.
• Polynomial containing degree 4 is know as Quartic Polynomial.