Question

if one zero of 3x²+8x+k be the reciprocal of the other than k=
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Answer 1

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 :

• Given quadratic polynomial : 3x² + 8x + k

• To find : k = ?

Now ,

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

a = 3

b = 8

c = k

Also ,

It is given that , one of the zero of the given quadratic polynomial is reciprocal of another .

Thus ,

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

Now ,

We know that ,

=> Product of zeros = c/a

=> α•(1/α) = k/3

=> 1 = k/3

=> k = 3

Hence , k = 3 .