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Question

# For the equation ax2+bx+c=0, a,b and c are real,Statement 1: If the equation ax2+bx+c=0,0<a<b<c, has non-real complex roots z1 and z2, then |z1|>1,|z2|>1.Statement 2: Complex roots always occur in conjugate pairs.

A
Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
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B
Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.
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C
Statement 1 is true and Statement 2 is false.
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D
Statement 1 is false and Statement 2 is true.
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Solution

## The correct option is A Both the statements are true, and Statement 2 is the correct explanation for Statement 1.If roots of ax2+bx+c=0, 0 < a < b < c, are nonreal, then they will be the conjugate of each other. Hence,z2=¯¯¯z1⇒|z1|=|z2|Now, z1z2=ca>1⇒|z1|2>1⇒|z1|>1⇒|z2|>1

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