Question

Find a quadratic polynomial the sum and product of whose zeroes are √2 and 1/3. (Maths Class X)​

Answer 1

▪Given :-

For a Quadratic Polynomial

• Sum of Zeros = √3

• Product of Zeros = 1/3

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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 :-

$\large\pink{ \bf  {x}^{2}  - s \: x + p}$

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▪Solution :-

Here,

Sum = s = √2

and

Product = p = 1/3

So,

Required Polynomial should be

$\bf{x}^{2}  -  \sqrt{2}x+\dfrac{1}{3}$

i.e.

$\Large\color{magenta} \bf 3 {x}^{2}  -3\sqrt{2}x +1$

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

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