Find quadratic polynomial whose sum of zero and products of zero hour respectively 4 and 1.​

1 thought on “Find quadratic polynomial whose sum of zero and products of zero hour respectively 4 and 1.​”

1. [tex]\large {\pmb{\mathfrak{\red{Given…}}}}[/tex]

   Given that, 4 and 1 are the sum and product of the zeroes of a polynomial respectively.

   [tex] \\ [/tex]

   [tex]\large {\pmb{\mathfrak{\red{To~ find…}}}}[/tex]

   We have to find the polynomial.

   [tex] \\ [/tex]

   [tex]\large {\pmb{\mathfrak{\red{Solution…}}}}[/tex]

   According to the question,

   • Sum of zeroes = 4 = : [tex]\sf \alpha+\beta[/tex]
   • Product of zeroes = 1 : [tex]\sf \alpha\beta[/tex]

   We know that :

   [tex]\underline{\pmb{\bf{\green{Polynomial= x^2-(Sum~of~ the ~ zeroes)x+(Product~of ~ the ~zeroes)}}}}[/tex]

   Now, from the question, we’ll substitute the sum and product of the zeroes in the formula above and form the polynomial :

   [tex]:\implies \sf x^2-(\alpha+\beta)x+(\alpha\beta)[/tex]

   [tex] : \implies \sf {x}^{2} – (4)x + (1)[/tex]

   [tex] : \implies\sf {x}^{2} – 4x + 1[/tex]

   ____________________

   [tex]\pmb{\bf{\green{\therefore~x^2-4x+1~is~the~required~polynomial.}}}[/tex]

   [tex]\\[/tex]

   [tex]\large {\pmb{\mathfrak{\red{Important~points…}}}}[/tex]

   • [tex]\sf \alpha+\beta+\gamma=\dfrac{-b}{a}[/tex]

   • [tex]\sf \alpha\beta\gamma=\dfrac{-d}{a}[/tex]

   • [tex]\sf \alpha\beta+\beta\gamma+\gamma\alpha=\dfrac{c}{a}[/tex]

   • Quadratic formula = [tex]\sf \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

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