Math, asked by sawantshatakshi1126, 7 months ago

form the quadratic equation if its roots are -13 and 6

Answers

Answered by prince5132

GIVEN :-

Roots of a quadratic equation are -13 and 6.

TO FIND :-

The required quadratic equation.

SOLUTION :-

As we know that the quadratic polynomial is given by,

$\\ : \implies \displaystyle \sf \: x ^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0 \\ \\$

ɑ = -13
β = 6

$\\ \\ : \implies \displaystyle \sf \: x ^{2} - ( - 13 + 6)x + ( - 13 \times 6) = 0 \\ \\ \\$

$: \implies \displaystyle \sf \: x ^{2} - ( - 7)x + ( - 78) = 0 \\ \\ \\$

$: \implies \underline{ \boxed{ \displaystyle \sf \bold{ \: x ^{2} + 7x - 78 = 0}}} \\ \\$

Hence the required polynomial is x² + 7x - 78 = 0.

ADDITIONAL INFORMATION :-

$\boxed{\begin{minipage}{5.5 cm} {$\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}}$

Answered by sara122

Answer:

$\huge\mathfrak\red{\bold{\underline{☯︎{Lεศɢนε \: σʄ \: Mıŋɖร}☯︎ }}}$ $\huge\underbrace\mathscr\color{lime}{ †\: Solution:–}$

GIVEN :-

Roots of a quadratic equation are -13 and 6.

TO FIND :-

The required quadratic equation.

SOLUTION :-

As we know that the quadratic polynomial is given by,

$\sf\green{= > x^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0}$

$\pink\alpha = - 13$
$\pink \beta = 6$

$\sf \red{= > x {}^{2} - ( - 13 + 6)x + ( - 13 \times 6) = 0}$

$\sf \purple{= > {x}^{2} - ( - 7)x + ( - 78) = 0}$

$\sf \pink {= > {x}^{2} + 7x - 78 = 0}$

$\huge\orange{\boxed{\blue{\bold{\fcolorbox{orange}{yellow}{\orange{Hope\:It\:Helps༒}}}}}}$ $\huge\orange{\underline\blue{\underline\green{\underline{ \mathtt\blue{Please}\:\mathtt\green{Mark}\:\mathtt\orange{As}}}}}$

$\huge\orange{\underline\blue{\underline\green{\underline{ \mathtt\red{Brilliant}\:\mathtt\purple{Answers}}}}}$

$\huge\orange{\underline\blue{\underline\green{\underline{ \mathcal\orange{Thank}\:\mathcal\green{You}}}}₪}$

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form the quadratic equation if its roots are -13 and 6​

Answers

GIVEN :-

TO FIND :-

SOLUTION :-

form the quadratic equation if its roots are -13 and 6