Question

the sum and product of zeros of a quadratic polynomial are 3 and -10 respectively. the polynomial is ?

Answer 1

EXPLANATION

• GIVEN

Sum of zeroes of quadratic equation =

a + b = 3

Product of zeroes of quadratic equation =

ab = -10

EQUATION OF QUADRATIC POLYNOMIAL

x^2 - (a + b) x + ab

x^2 - 3x -10 = 0 => ANSWER

SOME RELATED FORMULA

For quadratic polynomial

x^2 - (a + b) x + ab

For cubic polynomial

x^3 - ( a + b +c) x^2 + (ab + bc + ca) x - abc

Answer 2

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

• Sum of Zeroes ( α + β ) = 3
• Product of Zeroes ( αβ ) = -10
• Quadratic Polynomial = ?

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

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

$:\implies\sf Polynomial=x^2-(Sum\:of\:Zeroes)x+Product\:of\:Zeroes\\\\\\:\implies\sf Polynomial=x^2 -(\alpha + \beta)x + ( \alpha \beta)\\\\\\:\implies\sf Polynomial=x^2 - ( 3 )x + (-10)\\\\\\:\implies\underline{\boxed{\sf\pink{ Polynomial=x^2 -3x -10}}}$

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$\therefore\:\underline{\textsf{Required polynomial is \textbf{x ^\text2 -3x -10}}}.$

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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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