Question

Find a quadratic equations if the sum and product of zeroes respectively: √2,1/3

Answer 1

$\large \bf \clubs \:  Given :-$

For a Quadratic Equation :

   

• Sum of Zeros = √2

• Product of Zeros = 1/3

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$\large \bf \clubs \:   To  \: Find :-$

• The Quadratic Equation.

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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 Equation is given by :-

$\large\bf  {x}^{2}  - S \: x + P=0$

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$\large \bf \clubs \:  Solution  :-$

Here,

• Sum = S = √2

• Product = P = 1/3

So,

Required Equation should be :

$\bf  {x}^{2}  - S \: x + P=0$

$:\longmapsto  \tt{x}^{2}  - \sqrt{2} x + \dfrac{1}{3}=0$.

$\Large\purple{:\longmapsto\pmb{3{x}^{2}  -3\sqrt{2}\:x +1=0}}$

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

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Answer 2

Step-by-step explanation:

$\purple{ \sf \clubs \:Given : } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \: A \: Quadratic \: equation : \: \: \: \\ \mapsto\sf Sum \: of \: zeroes = \sqrt{2} \: \: \: \\ \mapsto \sf Product \: of \: zeroes = \frac{1}{3} \\ \purple{ \huge{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \purple{ \sf \clubs \:To \: find : } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf The \: Quadratic \: Equation \\ \purple{ \huge{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \purple{ \sf \clubs \: Main \: Concept : } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\purple{\bigstar} \: If \: sum \: and \: products \: of \\ \sf zeroes \: of \: any \: quadratic \: polynomial \\ \sf are \: taken \: as \: S \: and \: P \: respectively, \\ \sf \: then \: the \: quadratic \: equation \: is \\ \sf \: given \: by : \\ \purple{\bf {x}^{2} - Sx + P = 0} \\ \purple{ \huge{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \sf\purple{ \clubs \: Solution :} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf S = \sqrt{2} \\ \sf P = \frac{1}{3} \\ \sf So,\: Required \: Equation \: is : \\ \sf {x}^{2} - Sx + P = 0 \\ \sf \longmapsto \: {x}^{2} - \sqrt{2} x + \frac{1}{3} = 0 \\ \sf \longmapsto \: 3{x}^{2} - 3\sqrt{2} x + 1 = 0 \\ \sf \orange{Which \: is \: the \: required} \\ \sf \orange{Answer \: .} \\ \purple{ \huge{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}$