Question

Q. 2 - Find a quadratic polynomial whose zeros are 3+V5 and 3-V5​

Answer 1

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✪QUESTION✪:-

Find a quadratic polynomial

whose zeros are 3+√5 and 3-√5

✪ANSWER✪:-

SUM OF THE ZEROS :-

➠3+√5 + 3-√5

➠6

PRODUCT OF ZEROS :-

➠(3+√5) (3-√5)

it is in the form of (a+b) (a-b)

USING IDENTITY:

$\boxed{\sf{a²-b² = (a+b) (a-b)}}$

here ,

• a = 3
• b = √5

so,

➠(3+√5) (3-√5)

➠(3)² - (√5)²

➠9 - 5

➠4

QUADRATIC EQUATION FORMAT :

➠x² - (sum of zeros) x + ( product of zeros )

by sub/: values in the format ,we get

$\boxed{\sf{x² - 6x + 4 }}$

◆ ━━━━❪✪❫━━━━ ◆

ABOUT ZERO OF POLYNOMIAL :

The zero of the polynomial is the value that we use in that sum which makes the polynomial equal to zero .

FOR EXAMPLE :

In above equation

$\boxed{\sf{x² - 6x + 4 }}$

we said that

• 3+√5
• 3-√5

are zeros of polynomial .

let's verify whether the values are zero of the given polynomial

➥3+√5 :-

➠x² - 6x + 4

➠(3+√5)² -6(3+√5) +4

(3+√5)² is in the form of (a+b)²

USING IDENTITY:

$\boxed{\sf{(a+b)² = a²+ b² +2ab}}$

here ,

• a = 3
• b = √5

➠(3+√5)² -6(3+√5) +4

➠(9 + 5 + 2(3)(√5) ) -18 - 6√5 +4

➠14 + 6√5 -18 - 6√5 +4

➠0

• thus ,3+√5 is the one of the zero of the polynomial as the value make this polynomial equal to zero .

• similarly we get same result with 3-√5