Question

Find the quadrilateral polynomial with each the given number as the sum and product of its zeros -3 and -2 respectively

Answer 1

AnsWer :

x² + 3x + 2.

Correct QuestioN :

Find the quadratic polynomial with each the given number as the sum and product of its zeros - 3 and 2 respectively.

To FinD :

The quadratic polynomial

SolutioN :

We have, zeros

★ Sum of Zero = - b / a = - 3.

★ Product of Zeros = c / a = 2.

We know,

K [ x² + Sx + P ]

where as,

• S Sum of Zero.
• P Product of Zero.
• K content term.

Now, putting the given value on it.

→ K[ x² - ( - 3 )x + ( 2 ) ]

→ K[ x² + 3x + 2 ]

Therefore, the quadratic polynomial is x² + 3x + 2.

$\rule{200}3$

VerificatioN :

Taking Equation,

• x² + 3x + 2.

→ x² + 3x + 2.

→ x² + 2x + x + 2.

→ x( x + 2 ) + 1 ( x + 2 )

→ ( x + 1 )( x + 2 )

___________

→ x + 1 = 0.

→ x = - 1.

___________

→ x + 2 = 0.

→ x = - 2.

Sum of the Zero

→ ( - 1 ) + ( - 2 ) = - b / a.

→ - 1 - 2 = - 3 / 1.

→ - 3 = - 3.

Product Of Zeros

→ ( - 1 ) + ( - 2 ) = c / a.

→ - 1 - 2 = 2.

→ 2 = 2.

Hence Verified.

Answer 2

Step-by-step explanation:

QUESTION :-

Find the quadrilateral polynomial with each the given number as the sum and product of its zeros -3 and -2 respectively

ANSWER:-

We have, zeros

★ Sum of Zero = - b / a = - 3.

★ Product of Zeros = c / a = 2.

We know,

K [ x² + Sx + P ]

where as,

S Sum of Zero.

P Product of Zero.

K content term.

Now, putting the given value on it.

→ K[ x² - ( - 3 )x + ( 2 ) ]

→ K[ x² + 3x + 2 ]

Therefore, the quadratic polynomial is x² + 3x + 2.