Question

Find the quadratic polynomial if sum of roots are -2and the product of roots are 4

Answer 1

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▪Given :-

For a Quadratic Polynomial

   

Sum of Zeros = - 2

Product of Zeros = 4

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▪To Find :-

The Quadratic Polynomial.

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▪Key Point :-

If sum and product of zeros of any quadratic polynomial are s and p respectively,

Then,

The quadratic polynomial is given by :-

$\bf  {x}^{2}  - s \: x + p$

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▪Solution :-

Here,

Sum = s = - 2

and

Product = p = 4

So,

Required Polynomial should be

$\bf{x}^{2}  -(-2)x +4$

i.e.

$\Large\bf  {x}^{2}  +2x+4$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

x² + 2x + 4

Step-by-step explanation:

Given -

Sum of zeroes (roots) = -2

Product of zeroes = 4

To find -

The quadratic polynomial

Solution -

To find the polynomial, we use the formula,

x² - (sum of zeroes)x + (product of zeroes)

=> x² - (-2)x + 4

=> x² + 2x + 4

So the quadratic equation is x² + 2x + 4.

Note :-

A quadratic polynomial have only 2 zeroes.

zeroes are also known as roots.

The standard form of quadratic equation = ax² + bx + c

• a = coefficient of x²
• b = coefficient of x
• c = non variable number

Sum of zeroes = -b/a

Product of zeroes = c/a

hope it helps.