Question

if one zores of the polynomial x squared-4x+1 is (2+root 3 ),write the other zero
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Answer 1

Answer:

it's so easy

Step-by-step explanation:

3+√2

ok

it's so simple

Answer 2

Answer :

2 - √3

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution :

Here ,

The given quadratic polynomial is ;

x² - 4x + 1 = 0 .

Now ,

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c = 0 , we have ;

a = 1

b = -4

c = 1

Also ,

Let α = 2 + √3 (given) and ß be the zeros of the given quadratic polynomial .

Also ,

We know that , the sum of the zeros of a quadratic polynomial is given as ;

=> α + ß = -b/a

=> 2 + √3 + ß = -(-4)/1

=> 2 + √3 + ß = 4

=> ß = 4 - 2 - √3

=> ß = 2 - √3

Hence ,

The other zero of the given quadratic polynomial is (2 - √3) .