Find the quadrilateral polynomial with each the given number as the su

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

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

Answer»

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.