Question

6
Section - B
1.
· Fine a quadratic polynomial whose zeros are 4 and 2.​

Answer 1

Answer:

x2 - 6x +8

Step-by-step explanation:

alpha = 4

beta = 2

So,

alpha + beta = 4+2 = 6

alpha × beta = 4 × 2 =8

So,

quadratic polynomial = x2 - (alpha + beta) × x + alpha × beta

= x2 - 6x +8

Answer 2

The required quadratic polynomial whose zeroes are 4 , 2 is x² - 6x + 8

Given :

The zeroes of a quadratic polynomial are 4 , 2

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 , 2

Sum of zeroes = 4 + 2 = 6

Product of the zeroes = 4 × 2 = 8

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

$\displaystyle \sf = {x}^{2} -6x + 8$

Hence the required quadratic polynomial whose zeroes are 4 , 2 is x² - 6x + 8

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$1.$ If p(x) = 2x2 + 4x + 6 is a quadratic polynomial then what is the value of sum of zeroes?

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