Math, asked by abhinav1198, 11 months ago

Find the quadratic polynomial whose zeroes are 4 and (-4).​

Answers

Answered by pulakmath007
0

The quadratic polynomial whose zeroes are 4 , - 4 is x² - 16

Given :

The zeroes of a quadratic polynomial are 4 , - 4

To find :

The quadratic polynomial

Concept :

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 }

Solution :

Step 1 of 2 :

Find Sum of zeroes and Product of the zeroes

Here it is given that zeroes of a quadratic polynomial are 4 , - 4

Sum of zeroes = 4 + ( - 4 ) = 4 - 4 = 0

Product of the zeroes = 4 × ( - 4 ) = - 16

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

\displaystyle \sf{ =  {x}^{2}  - 0.x + ( - 16)  }

\displaystyle \sf{ =  {x}^{2}  - 16}

Hence the quadratic polynomial whose zeroes are 4 , - 4 is x² - 16

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