Question

Find a quadratic polynomial whose zeroes are 7-2√3 and 7+2√3.​

Answer 1

α=7-2√3

β=7+2√3

α+β=7-2√3 +7+2√3

     =14

αβ=(7-2√3 )(7+2√3)

   =7²-(2√3)²

   =49-12

   =37

the quadratic polynomial is x²-14x+37

Answer 2

Answer:

The quadratic polynomial is (x - 7 - 2√3) (x - 7 + 2√3) = $x^{2}$  -  14x   + 49.

Question : Find a quadratic polynomial whose zeroes are 7-2√3 and 7+2√3.​

Step-by-step explanation:

From the above question,

They have given :

7-2√3 and 7+2√3.​

A quadratic polynomial is a polynomial of degree 2, meaning it is a polynomial equation with terms of degree 2 or lower. It can be written in the form ax2 + bx + c, where a, b, and c are constants, and a is not equal to 0.

To Identify the zeroes :

  The zeroes are 7-2√3 and 7+2√3.

Write the polynomial   :

The polynomial is (x - (7 - 2√3))(x - (7 + 2√3)).

Simplify the polynomial.

The polynomial simplifies to x2 - 14x + 49 - 24√3.

Hence,

The quadratic polynomial is (x - 7 - 2√3) (x - 7 + 2√3) = $x^{2}$  -  14x   + 49.

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