Answér :

x² + x - 6

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 are the zeros of the required quadratic polynomial .

Thus ,

Let α = -3 and ß = 2

Now ,

Sum of zeros of the required quadratic polynomial will be ;

α + ß = -3 + 2 = -1

ALSO ,

Product of zeros of the required quadratic polynomial will be ;

αß = -3×2 = -6

Thus ,

The required quadratic polynomial polynomial will be ;

=> k•[ x² - (α + ß)x + αß ]

=> k•[ x² - (-1)x + (-6) ]

=> k•[ x² + x - 6 ]

For k = 1 , the polynomial will be ;

x² + x - 6

Hence ,

Required answer is : x² + x - 6