Question

Write a quadratic polynomal, the
sum and product of whose zeroes
are 3 and -2 respectively​

Answer 1

Answer:

alpha + bheta = sum of zeros = 3 = -b/a

alpha × bheta = product of zeros = -2 = c/a

by comparing a = 1 , b= -3 , c = -2

quadratic polynomial = ax^2 + bx + c

x^2 -3x -2

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Answer 2

AnswEr :

x² - 3x - 2.

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

The sum and product of whose zeroes are 3 and -2 respectively.

$\bf{\green{\underline{\underline{\bf{To\:find\::}}}}}$

A quadratic polynomial.

$\bf{\green{\underline{\underline{\bf{Explanation\::}}}}}$

We have sum of zeroes = 3

$\star{\purple{\underline{\bf{Sum\:of\:the\:zeroes\::}}}}$

$\leadsto\sf{\alpha +\beta=\dfrac{-b}{a} =\dfrac{Coefficient\:of\:(x)^{2} }{Coefficient\:of\:x} }\\\\\\\leadsto\sf{\red{\alpha +\beta =3}}$

We have product of zeroes = -2

$\star{\purple{\underline{\bf{Product\:of\:the\:zeroes\::}}}}$

$\leadsto\sf{\alpha +\times \beta=\dfrac{c}{a} =\dfrac{Constant\:term }{Coefficient\:of\:x} }\\\\\\\leadsto\sf{\red{\alpha \times \beta =-2}}$

Now;

$\star\:{\underline{\underline{\bf{The\:quadratic\:polynomial\:required\::}}}}}}$

$\mapsto\sf{x^{2} -(sum\:of\:the\:zeroes)x+(product\:of\:the\:zeroes)}\\\\\mapsto\sf{x^{2} -(3)x+(-2)}\\\\\mapsto\sf{\red{x^{2} -3x-2}}$