MathematicsFind the quadratic polynomial, the sum and product of whose zeros are −3   and 2   respectively.

Find the quadratic polynomial, the sum and product of whose zeros are 3   and 2   respectively.


  1. A
    x2+3x+2
  2. B
    x2+3x-2
  3. C
    x2-3x-2
  4. D
    x2-3x+2 

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    Solution:

    Given that the sum of zeroes and product of zeroes of a quadratic polynomial is 3   and 2   respectively. We need to find the quadratic polynomial.
    A quadratic polynomial is of the form a x 2 +bx+c.  
    Let us assume the zeroes of the polynomial be α&β.  
    Based on the relationship between zeroes and polynomials we have quadratic polynomial as:
    p(x)= x 2 (α+β)x+αβ.....(i)  
    Now we have,
    α+β=3  
    αβ=2  
    Substituting the values in equation (i) we have,
    p(x)= x 2 (3)x+2 p(x)= x 2 +3x+2  
    Hence, the quadratic polynomial is x 2 +3x+2  .
    Therefore, option 1 is correct.
     
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