what is the quadratic polynomial whose sum and the product of zeroes is root2, 1/2 respectively​

2 thoughts on “what is the quadratic polynomial whose sum and the product of zeroes is root2, 1/2 respectively​”

1. Answer:

   FINDING POLYNOMIAL USING FORMULA-x²-(sum of zeroes)x+product of zeroes

   =x²-root2x+1/2

   =2x²-root2x+1. (takin 2 out of bracket)

   Step-by-step explanation:

   polynomial is 2x²-root2x+1

   HOPE THIS WILL HELP YOU!

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2. ☯GIVEN :

   • [tex] \alpha + \beta = \sqrt{2} [/tex] and [tex]\alpha \beta = \dfrac{1}{2}[/tex] .

   ☯TO FIND :

   • Quadratic Polynomial.

   ☯FORMULA REQUIRED :

   • [tex]\underline{\boxed{\purple{\bf{x^2- \left(\alpha + \beta\right)x + \alpha\beta =0 }}}} [/tex]

   ➲SOLUTION :

   We have,

   • By substituting the values, [tex] \alpha + \beta = \sqrt{2} [/tex] and [tex]\alpha \beta = \dfrac{1}{2}[/tex] :

   [tex]:\implies {\sf x^2 – \left(\alpha + \beta \right)x + \alpha \beta = 0}\\ \\ [/tex]

   [tex]:\implies {\sf x^2- (\sqrt{2} )x+\dfrac{1}{2} =0 }\\ \\ [/tex]

   [tex]:\implies {\sf x^2- \sqrt{2} x+\dfrac{1}{2 } =0 }\\ \\ [/tex]

   [tex]:\implies {\sf \dfrac{2 x^2 – 2\sqrt{2} x + 1}{2} =0 }\\ \\ [/tex]

   • By cross multiplication :

   [tex]:\implies {\sf 2 x^2 – 2\sqrt{2} x + 1 = 0 \times 2} \\ \\ [/tex]

   [tex]:\implies{ \underline{ \boxed{ \blue{\bf{ 2 x^2 – 2\sqrt{2} x + 1 = 0}}}}}[/tex]

   [tex]\huge{\green{\therefore}}[/tex] Quadratic Polynomial = [tex]\bf{ 2 x^2 – 2\sqrt{2} x + 1 }[/tex].

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