Math, asked by rupali96, 1 year ago

06. Find a quadratic polynomial whose zeroes are 5 + √2 and 5 - √2.​

Answers

Answered by Anonymous
2

Heya!!

let the Quadratic polynomial be F(x)

F(x) = - (Sum of zeros)x + (product of zeros)

Here, Sum of zeros = 5 + 2 + 5 -2

Sum of zeros = 10

And

product of zeros = (5 + 2 ) (5 -2)

product of zeros = (5)² - (2)²

product of zeros = 25 - 2 = 23

So, Quadratic polynomial is

F(x) = - (10)x + 23

F(x) = - 10x + 23

Note:-

F(x) = - (Sum of zeros)x + product of zeros. is the general formula to form a Quadratic polynomial when roots are given.

(a + b) (a - b) = -

Answered by LovelyG
2

Answer:

x² - 10x + 23

Step-by-step explanation:

Given that -

Roots of the quadratic equation are (5 + √2) and (5 - √2). Let us consider the roots of the equation be α and β. Thus,

α = (5 + √2) and β = (5 - √2),

Now, find the value of (α + β) -

α + β = 5 + √2 + 5 - √2

⇒ α + β = 5 + 5

⇒ α + β = 10

Also, find the value of (αβ) -

αβ = (5 + √2)(5 - √2)

⇒ αβ = (5)² - (√2)²

⇒ αβ = 25 - 2

⇒ αβ = 23

We know that;

Quadratic polynomial is given by-

= x² - (α + β)x + αβ

= x² - 10x + 23

Hence, the required quadratic polynomial is x² - 10x + 23.

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