Find all real values of a such that

loraliyeruxi

loraliyeruxi

Answered question

2022-04-02

Find all real values of a such that x2+(a+i)x5i=0 has at least one real solution.

Answer & Explanation

Jared Kemp

Jared Kemp

Beginner2022-04-03Added 14 answers

If p and q are the roots of x2+(a+i)x5i=0, then p+q=(a+i) and pq=5i. If p is real, then q=5ip is imaginary. If a is real, then we must have q=i and p=a. We find p=5iq=5, hence a=5 is the only real number for which x2+(a+i)x5i=0 has a real root.
The equations p+q=(a+i) and pq=5i come from expanding (xp)(xq)=x2(p+q)x+pq and equating coefficients with those of x2+(a+i)x5i.

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