Question

obtain a quadratic polynomial if sum of zeroes =-3 ;. and product of zeroes = -4​

Answer 1

Question:

Obtain a quadratic polynomial if sum of zeroes is -3 and product of zeroes is -4.

Solution:

Let,

we have to obtain a polynomial

ax^2 + bx + c

then,

as given

-3 = sum of zeroes

-3 = -b/a

-(3) /1 = -(b) /a

and

-4 = product of zeroes

-4 = c/a

(-4) /1 = (c) /a

On comparison we will get

a = 1 ; b = 3 ; c = -4

Hence,

our quadratic polynomial will be

ax^2 + bx + c

(1) x^2 + (3) x + (-4)

therefore,

x^2 + 3x - 4

is the required polynomial.

Answer 2

❏ SolutioN :

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$\blacksquare\:\:\footnotesize{\underline{\underline{Given}}}$

$\footnotesize{product\: of \:zeroes = -4}$

$\footnotesize{sum\: of \:zeroes = -3}$

$\blacksquare\:\:\footnotesize{\underline{\underline{To\: Find}}}$

$\footnotesize{find \:the\: quadratic\: equation}$

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$\footnotesize{\text{we know that for a quadratic equation }if\: \alpha\: and\: \beta}$

$\footnotesize{ \text{are the zeroes of the equation then the quadratic equation is :}}$

$\longrightarrow\footnotesize{ x^2-(\alpha+\beta)x+\alpha\beta=0}$

$\footnotesize{\alpha+\beta=-3 \:and\: \alpha\beta = -4 }$

$\therefore\footnotesize{Quadratic \: polynomial\:is \:,}$

$\footnotesize{=x^2-(-3)x+(-4)}$

$\footnotesize{\boxed{=x^2+3x-4}}$

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