If the squared difference of the zeros find the value of p, Mathematics

If the squared difference of the zeros of the quadratic polynomial x2 + px + 45 is equal to 144 , find the value of p.                                                                                                                (Ans: ± 18).

Ans:  Let two zeros are α and β where α > β

According given condition

(α - β)2 = 144

Let p(x) = x2 + px + 45

α + β = -b/a = -p /1 = - p

αβ =  c/a = 45/1 = 45

now (α - β)2 = 144

(α + β)2 - 4 αβ = 144

(-p)2 - 4 (45) = 144

Solving this we get    p = ± 18

Posted Date: 4/8/2013 1:56:51 AM | Location : United States







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