Question

نا
write a
quadratic polynomial the sum and product of
whose
are 3
and 2​

Answer 1

AnsWer :

x² - 3x + 2.

SolutioN :

☯ Condition :

• Sum of Zeros : 3
• Product Of Zeros : 2.

☯ We know, that.

→ K[ x² - Sx + P ]

• Where as,
• S Sum of Zeros.
• P Product of Zero.
• K Constant term.

→ K[ x² - ( Sum of Zeros )x + ( Product of Zero ) ]

→ 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 - 2x - x + 2.

→ x( x - 2 ) - 1( x - 2 )

→ ( x - 1 )(x - 2 )

$\rule{90}2$

✎ Either,

→ x - 1 = 0.

→ x = 1.

$\rule{90}2$

✎ Or,

→ x - 2 = 0.

→ x = 2.

$\rule{90}2$

Let,

• Zeros be,
• α and β.

☛ Sum of Zeros.

→ α + β.

→ 1 + 2

→ 3.

$\rule{90}2$

☛ Product Of Zeros.

→ α * β

→ 1 * 2

→ 2.

Hence Verify.