Question

if sum of zeros of a quadratic polynomial is 10 and product of zeros is 39 then find polynomial​

Answer 1

Answer:

from Formulae....X²-(a+b)x+ab where a and b are roots then x²-10x+39 is the polynomial where sum and Products are given in the Question it self

Answer 2

$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \large\mathfrak{\dag \: Given : }\:\:\:\:\:\:\:\:\:\:\:\:\:\:$

• Sum of Zeroes ( α + β ) = 10
• Product of Zeroes ( αβ ) = 39
• Quadratic Polynomial = ?

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \large\mathfrak{\dag \: Required \: Solution : }\:\:\:\:\:\:\:\:\:\:\:\:\:\:$

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Polynomial=x^2-(Sum\:of\:Zeroes)x+Product\:of\:Zeroes\\\\\\:\implies\sf Polynomial=x^2 -(\alpha + \beta)x + ( \alpha \beta)\\\\\\:\implies\sf Polynomial=x^2 - ( 10)x + 39\\\\\\:\implies\underline{\boxed{\sf\red{ Polynomial=x^2 -10x + 39}}}$

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$\therefore\:\underline{\textsf{Required polynomial is \textbf{x ^\text2 -10x + 39}}}.$

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⠀⠀⠀⠀⠀$\rule{180}{1.5}$

$\boxed{\begin{minipage}{5.5 cm} { \bigstar\: \textsf{For a Quadratic Polynomial :}}\\\\ {\qquad\sf p(x) = ax ^\sf2 \sf + bx + c}\\\sf with zeroes \alpha\:\sf and\:\beta \\\\\\ {\textcircled{\footnotesize1}} \:\:\alpha +\beta= \dfrac{ - \:b}{a}\:\:\bigg\lgroup\bf Sum\:of\:Zeroes\bigg\rgroup \\\\\\{\textcircled{\footnotesize2}} \: \:\alpha \beta= \sf\dfrac{c}{a}\:\:\bigg\lgroup\bf Product\:of\:Zeroes\bigg\rgroup\end{minipage}}$

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