Question

If zero of polynomial is 3x^2+9x+K then I find the reciprocal of K=?​

Answer 1

Question :

If the zeros of the polynomial 3x² + 9x + k are reciprocal of each other then find the value of k .

Answer :

k = 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 ;

3x² + 9x + k .

Now ,

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

a = 3

b = 9

c = k

Also ,

It is given that , the zeros of the given quadratic polynomial are the reciprocal of each other .

Thus ,

Let α and 1/α are the zeros of the given quadratic polynomial .

Now ,

=> Product of zeros = c/a

=> α × 1/α = k/3

=> 1 = k/3

=> k = 3

Hence , k = 3 .

Answer 2

3 is the zero of 3x²+(k−3)x+9x=0

Therefore,

27+3k−9+27=0

3k+45=0

3k=−45

k=−15