Question

Find the quadratic polynomial, whose zeroes are 5 and -8.

Answer 1

Given, x = 5 &x = -8

Therefore, (x-5) = 0 & (x+8)= 0

Multiplying both terms

(x-5) (x+8)

x² + 8x - 5x - 40

x² + 3x -40

Hence, it is required quadratic polynomial.

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Answer 2

The required quadratic polynomial whose zeroes are 5 and - 8 is x² + 3x - 40

Given :

The zeroes of a quadratic polynomial are 5 and - 8

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 5 and - 8

Sum of zeroes = 5 + ( - 8 ) = 5 - 8 = - 3

Product of the zeroes = 5 × ( - 8 ) = - 40

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

$\displaystyle \sf = {x}^{2} -(-3)x + (-40)$

$\displaystyle \sf = {x}^{2} +3x - 40$

Hence the required quadratic polynomial whose zeroes are 5 and - 8 is x² + 3x - 40

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