Question

Find a quadratic polynomial, the sum and product of whose zeroes are 0 and 2, respectively​

Answer 1

$\textbf{Given:}$

$\textsf{Sum of zeroes=0}$

$\textsf{Product of zeroes=2}$

$\textbf{To find:}$

$\textsf{The quadratic polynomial}$

$\textbf{Solution:}$

$\textsf{The required quadratic polynomial is}$

$\mathsf{x^2-(Sum\;of\;zeroes)x+Product\;of\;zeroes}$

$\mathsf{x^2-(0)x+2}$

$\implies\boxed{\mathsf{x^2+2}}$

$\textbf{Find more:}$

Find the zeroes of the quadratic polynomial x2-15x+50 and verify the relationship between the zeroes and the coefficients of the polynomial​

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Answer 2

SOLUTION

TO DETERMINE

The quadratic polynomial when the sum and product of whose zeroes are 0 and 2 respectively

CONCEPT TO BE IMPLEMENTED

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

EVALUATION

Here it is given that for the given given polynomial

Sum of the zeroes = 0

Product of the Zeros = 2

Hence the required polynomial

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

$= \sf{ {x}^{2} - 0.x + 2 }$

$= \sf{ {x}^{2} + 2 }$

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