Question

Find a quadratic polynomial whose zeros are root 7 + root 11 and root 7 - root 11 .

Answer 1

Step-by-step explanation:

hope the above answer will help you

Answer 2

Answer :

x² - 2√7x - 4

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

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as :

k•[ x² - (α + ß)x + αß ] , k ≠ 0.

Solution :

Here ,

The given zeros of required quadratic polynomial are : (√7 + √11) , (√7 - √11) .

Let α = √7 + √11 and ß = √7 - √11

Now ,

Sum of zeros of required quadratic polynomial will be ;

=> α + ß = (√7 + √11) + (√7 - √11)

=> α + ß = 2√7

Also ,

Product of zeros of the required quadratic polynomial will be ;

=> αß = (√7 + √11)•(√7 - √11)

=> αß = (√7)² - (√11)²

=> αß = 7 - 11

=> αß = -4

Now ,

The general quadratic polynomials with zeros (√7 + √11) and (√7 - √11) will be given as ;

=> k•[ x² - (α + ß)x + αß ] , k ≠ 0

=> k•[ x² - 2√7x + (-4) ] , k ≠ 0

=> k•[ x² - 2√7x - 4 ] , k ≠ 0

For k = 1 , the quadratic polynomial will be ; x² - 2√7x - 4 .

Hence ,

Required quadratic polynomial is ;

x² - 2√7x - 4