Find the quadratic polynomial the sum and product of whose zeroes are respectively -10 and -39.
Answers
\:\:\:\:\:\:\:\:\:\:\:\:\:\: \large\mathfrak{\dag \: Given : }\:\:\:\:\:\:\:\:\:\:\:\:\:\:
\:\:\:\:\:\:\:\:\:\:\:\:\:\: \large\mathfrak{\dag \: Given : }\:\:\:\:\:\:\:\:\:\:\:\:\:\:
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Sum of Zeroes ( α + β ) = 10
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Product of Zeroes ( αβ ) = 39
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Quadratic Polynomial = ?
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\:\:\:\:\:\:\:\:\:\:\:\:\:\: \large\mathfrak{\dag \: Required \: Solution : }\:\:\:\:\:\:\:\:\:\:\:\:\:\:
\:\:\:\:\:\:\:\:\:\:\:\:\:\: \large\mathfrak{\dag \: Required \: Solution : }\:\:\:\:\:\:\:\:\:\:\:\:\:\:
\begin{gathered} \\\end{gathered}
\begin{gathered} \\\end{gathered}
\begin{gathered}\underline{\bigstar\:\textsf{According to the given Question :}}\\\\\end{gathered}
\begin{gathered}\underline{\bigstar\:\textsf{According to the given Question :}}\\\\\end{gathered}
\begin{gathered}:\implies\sf Polynomial=x^2-(Sum\:of\:Zeroes)x+Product\:of\:Zeroes\\\\\\:\implies\sf Polynomial=x^2 -(\alpha + \beta)x + ( \alpha \beta)\\\\\\:\implies\sf Polynomial=x^2 - ( 10)x + 39\\\\\\:\implies\underline{\boxed{\sf\red{ Polynomial=x^2 -10x + 39}}}\end{gathered}
\begin{gathered}:\implies\sf Polynomial=x^2-(Sum\:of\:Zeroes)x+Product\:of\:Zeroes\\\\\\:\implies\sf Polynomial=x^2 -(\alpha + \beta)x + ( \alpha \beta)\\\\\\:\implies\sf Polynomial=x^2 - ( 10)x + 39\\\\\\:\implies\underline{\boxed{\sf\red{ Polynomial=x^2 -10x + 39}}}\end{gathered}
Answer:
x^2+10x-39
Step-by-step explanation:
Quadratic polynomial = x^2-(sum of zeroes)x +(product of zeroes).
= x^2-(-10)x+(-39)
x^2+10x-39