Question

A quadratic polynomial with sum and product of its zeroes as -5 and 6 respectively is
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Answer 1

$\large \bf \clubs \:  Given :-$

For a Quadratic Polynomial :

• Sum of Zeros = -5

• Product of Zeros = 6

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$\large \bf \clubs \:   To  \: Find :-$

• The Quadratic Polynomial.

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$\large \bf \clubs \:   Main  \:  Concept : -$

✏ If sum and product of zeros of any quadratic polynomial are S and P respectively,

Then,

The quadratic polynomial is given by :-

$\large\bf  {x}^{2}  - S \: x + P$

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$\large \bf \clubs \:  Solution  :-$

Here,

• Sum = S = -5

• Product = P =6

So,

Required Polynomial should be :

$\bf  {x}^{2}  - S \: x + P$

$:\longmapsto  \tt{x}^{2}  - (-5) x + 6$.

$\Large\purple{:\longmapsto\pmb{{x}^{2}  +5x +6}}$

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

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Answer 2

Step-by-step explanation:

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

♧♧Given:-

♧For a given quadratic polynomial

• Sum of zeroes = -5
• Product of zeroes = 6.

♧To prove :-

• We should find the quadratic polynomial.

♧Proof:-

Here we can take main concept as

• Lets take sum and product of zeroes Of quadratic polynomial be A and B.

• Then the quadratic polynomial be

x^2-Ax+B

• Where,

1. The sum = A=-5
2. The product =B=6.

♧♧Hence , here.

• Required quadratic polynomial be

x^2-Ax+B

• x^2 - (-5)x + 6

• x^2 + 5x + 6.

♧♧Hence , this is the one of the required answer