Question

The sum and product of zeros of a quadratic polynomial are 9/2 and 2 respectively, then
the quadratic polynomial is:

Answer 1

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♣ Given :-

For a Quadratic Polynomial

   

• Sum of Zeros = 9/2

• Product of Zeros = 2

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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 = 9/2

• Product = p = 2

So,

Required Polynomial should be

$\bf{x}^{2}  - \dfrac{9}{2} x + 2$.

$\Large\purple{:\longmapsto\pmb{2 {x}^{2}  -9x +4}}$

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

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Answer 2

Given :-

The sum and product of zeros of a quadratic polynomial are 9/2 and 2 respectively

To Find :-

Quadratic polynomial

Solution :-

We know that

Standard form of quadratic polynomial = x² - (α + β)x + αβ

α + β = -b/a

α + β = (9/2)

αβ = c/a

αβ = 2

x² - (9/2)x + 2

x² - 9x/2 + 2

2x² - 9x + 2

Hence

quadratic polynomial is 2x² - 9x + 2