MathematicsFind a quadratic polynomial, the sum and product of whose zeroes are −7   and −18   respectively. Also find the zeroes.

Find a quadratic polynomial, the sum and product of whose zeroes are 7   and 18   respectively. Also find the zeroes.


  1. A
    polynomial =2 x 2 13x17   and zeroes =2,9  
  2. B
    polynomial = x 2 +7x18   and zeroes =2,9  
  3. C
    polynomial = x 2 5x20   and zeroes =1,5  
  4. D
    polynomial =3 x 2 +6x+27   and zeroes =2,7   

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    Solution:

    Given that the sum and product of the zeroes of a polynomial are 7   and 18  respectively. We need to find the quadratic polynomial and its zeroes.
    General form of quadratic polynomial is given as: a x 2 +bx+c=0.  
    In splitting the middle term method we split the middle term of quadratic equation in a   and b   such that,
    a+b=   middle term
    a×b=  product of first and third term
    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=7  
    αβ=18  
    Equating the values in equation (i) we have,
    p(x)= x 2 7 x18 p(x)= x 2 +7x18  
    Now equating p(x)=0   we have,
    x 2 +7x18=0  
    Hence, the quadratic polynomial is x 2 +7x18=0  .
    Using the splitting the middle term approach, on the polynomial x 2 +7x18=0  , we have,
    x 2 +7x18=0 x 2 +9x2x18=0 x x+9 2 x+9 =0 x2 x+9 =0 x=2,9   Hence, the zeroes of the polynomial are 2,9.  
    Therefore, the quadratic polynomial is x 2 +7x18   and the zeroes are 2,9.  
    Therefore, option 2 is correct.
     
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