Question

Find a quadratic polynomial whose sum of zeros is 9 / 2 and product of zeros is 2 ​

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

Answer:

$\underline{\purple{\ddot {\Mathsdude}}}$

☆☆Answered by Rohith kumar maths dude: -

☆☆Given:-

Sum of zeroes =-9/2

product of zeroes =2

☆☆To prove :-

The quadratic polynomial.

☆☆Explanation: -

●We know that ,

P (x)=x^2-(sum of zeroes)x+Product of zeroes

P(x)= x^2 -9/2x+2

●Now multiply the numbers ,

P (x)= x^2-1×9/2x+2

P (x)=x^2-9/2x+2.

☆Now combined multiplied terms into a single fraction :-

P (x)= x^2+ -9/2x+2

☆Finding the common denominator

☆we get,

P (x)=2x^2/2-9x/2+2.2/2

●Finally we get,

▪P (x)= 2x^2-9x+4 /2

P (x)=2x^2-9x+4.(is the answer)

☆Hopeit helps u mate.

☆Thank you