What is the condition that the following equation has four

Alan Zavala

Alan Zavala

Answered question

2022-04-16

What is the condition that the following equation has four real roots?
(a1x2+b1x+c1)(a2x2+b2x+c2)=0
a. c1c2>0
b. a1c2<0
c. a2c1<0

Answer & Explanation

davelucasnp0j

davelucasnp0j

Beginner2022-04-17Added 16 answers

It is sufficient if a1c1<0 and a2c2<0.
If all 3 conditions hold then, multiplying the first and second a1c1c22<0 so a1c1<0.
Similarly, multiplying the first and third, a2c2c12<0 so a2c2<0.
Therefore if all three conditions hold there are four real roots. The roots may not all be different depending on the coefficients.

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