Question

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Find a quadratic polynomial such that sum of its zeros is 9/2 and product of its zeros is 2 .
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Answer 1

$\large \bf \clubs \:  Given :-$

For a Quadratic Polynomial :

   

• Sum of Zeros = 9/2

• Product of Zeros = 2

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$\large \bf \clubs \:  To \: Find :-$

• The Quadratic Polynomial.

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$\large \bf \clubs \:  Main \: Concept : -$

☆ If sum and product of zeros of any quadratic polynomial are S and P respectively,

Then,

The quadratic polynomial is given by :-

$\bf  {x}^{2}  - S \: x + P$

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$\large \bf \clubs \:  Solution :-$

Here,

• Sum = S = 9/2

• Product = P = 2

So,

Required Polynomial should be :

$\bf  {x}^{2}  - S \: x + P$

$:\longmapsto  \tt{x}^{2}  - \dfrac{9}{2} x + 2$.

$\Large\purple{:\longmapsto\pmb{2 {x}^{2}  -9x +4}}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

❍ Given that, sum of zeros of a polynomial is 9/2 and product of its zeros is 2 and we need to find the quadratic polynomial.

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☀️ To Find the quadratic polynomial we must know that ::

x² - Sx + P  

Where,

• S denotes the sum of zeros
• P denotes product of zeroes

Finding the Quadratic Polynomial :-

$\sf : \; \implies x^{2} - \dfrac{9}{2}x + 2$

$\sf : \; \implies \dfrac{2x^{2} - 9x+ 4}{2}$

$\sf : \; \implies 2x^{2} - 8x + ( - x ) + 4$

$\bf : \; \implies 2x^{2} - 9x + 4$

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• Henceforth, the required quadratic polynomial is 2x² - 9x + 4