Question

Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 2

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Answer 1

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Given :

• Sum of zeros is -3
• Product of zeros is 2

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To Find :

• Find the equation

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Solution :

We have formula :

$\large {\boxed{\sf{x^2 \: - \: (Sum)x \: + \: Product}}} \\ \\ \implies {\sf{x^2 \: - \: (-3)x \: + \: 2}} \\ \\ \implies {\sf{x^2 \: + \: 3x \: + \: 2}}$

• Polynomial is x² + 3x + 2

Answer 2

Answer:

Required polynomial is x^2 + 3x + 2.

Step-by-step explanation:

We know,

Any quadratic equation / polynomial can be written as x^2 - Sx + P( = 0 ), with respect to x.

*where S represents the sum of roots and P represents the product of roots.

Therefore the equation for this case should be :

= > x^2 - ( - 3 )x + 2

= > x^2 + 3x + 2

Method - 2

Let the roots are a and b.

Given,

a + b = - 3 = > b = ( - 3 - a )

ab = 2

= > ( - 3 - a )a = 2

= > - ( a + 3 )a = 2

= > a^2 + 3a = - 2

= > a^2 + 3a + 2 = 0

= > a^2'+ a + 2a + 2 = 0

= > a( a + 1 ) + 2( a + 1 ) = 0

= > a = - 1 or - 2

Roots are : - 1 and - 2 or - 2 and - 1 { in both the cases roots are same }

Equation ( Quadratic) can be written as ( x - a )( x - b ) , where a and b are roots.

= > ( x - ( - 2 ))( x - ( - 1 ) )

= > x^2 + 3x + 2