Prove the following for the given quadratic If the

Pasegeabe85xy

Pasegeabe85xy

Answered question

2022-03-31

Prove the following for the given quadratic
If the difference of the roots of x2px+q=0 is unity then prove that p24q=1 and p2=4q2=(1+2q)2

Answer & Explanation

Alannah Campos

Alannah Campos

Beginner2022-04-01Added 10 answers

You cannot prove it because second part is wrong. For example, the roots of x2x=0 are 0 and 1 so the hypothesis is satisfied. We do have p24q=1 but we do not have p2=4q2=(1+2q)2.
Actually, the difference between the roots is 1 if and only if p24q=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

Carter Lin

Beginner2022-04-02Added 13 answers

The second one is very likely supposed to be
p2+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.

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