Prove the following for the given quadraticIf the difference of the roots of x2−px+q=0 is unity then prove that p2−4q=1 and p2=4q2=(1+2q)2

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Prove the following for the given quadraticIf the difference of the roots of x2−px+q=0 is unity then prove that p2−4q=1 and p2=4q2=(1+2q)2

Alannah Campos · Accepted Answer

You cannot prove it because second part is wrong. For example, the roots of x2−x=0 are 0 and 1 so the hypothesis is satisfied. We do have p2−4q=1 but we do not have p2=4q2=(1+2q)2.Actually, the difference between the roots is 1 if and only if p2−4q=1. Perhaps there is a typo in the question and the first equality in p2=4q2=(1+2q)2 is supposed to be replaced by +.

Carter Lin · Accepted Answer

The second one is very likely supposed to bep2+4q2=(1+2q)2.To prove it, try to expand (1+2q)2 and then use the first result. You no longer need to think about the original quadratic for this part.

Prove the following for the given quadratic If the

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