Question

find a quadratic polynomial whose zeros are (5 - 3 root 2) and (5 + 3 root 2)​

Answer 1

AnsWer :

x² - 10x + 7.

GiveN :

The Zeros of Polynomial be,

• 5 - 3√2 and 5 + 3√2.

SolutioN :

Let,

• a = 5 - 3√2.
• b = 5 + 3√2.

♢ Find Out.

✎ Sum of Zeros.

→ a + b = ( 5 - 3√2 ) + ( 5 + 3√2 )

→ a + b = 10.

$\rule{90}2$

✎ Product Of Zeros

→ a * b = ( 5 - 3√2 )( 5 + 3√2 )

$\rule{90}2$

★ Apply Formula :

• ( a + b )( a - b ) = a² - b².

→ a * b = 5² - ( 3√2 )²

→ a * b = 25 - 18.

→ a * b = 7.

Now,

# K [ x² - Sx + P ]

Where as,

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

→ K [ x² - ( 10 )x + 7 ]

→ K [ x² - 10x + 7 ]

✡ Therefore, Quadratic polynomial become x² - 10x + 7.

Answer 2

Sum of zeros = 5 - 3√2 + 5 - 3√2

= 5 + 5

= 10

Product of zeros = (5 - 3√2) (5 + 3√2)

= (5)^2 - ( 3√2)^2

= 25 - 18 = 7

= x^2 - (sum)x + product

= x^2 - 10x +7