Write a quadratic polynomial ,the sum and product of whose zeros are 3 ans -2 respectively .
Answers
Answér :
x² - 3x - 2
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.
★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;
D = b² - 4ac
★ If D = 0 , then the zeros are real and equal .
★ If D > 0 , then the zeros are real and distinct .
★ If D < 0 , then the zeros are unreal (imaginary) .
Solution :
Here ,
It is given that , 3 and -2 respectively are the sum and product of the zeros of the required quadratic polynomial .
Thus ,
Sum of zeros of the required quadratic polynomial is ;
α + ß = 3
Also ,
Product of zeros of the required quadratic polynomial is ;
αß = -2
Thus ,
The required quadratic polynomial polynomial will be ;
=> k•[ x² - (α + ß)x + αß ]
=> k•[ x² - 3x + (-2) ]
=> k•[ x² - 3x - 2 ]
For k = 1 , the polynomial will be ;
x² - 3x - 2