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