If 0 < a < b < c and the roots α, β of the equation ax2 + bx + c = 0 are imaginary, thenOnly one correct answerA.|α|=|β| and |α|<1𝛼=𝛽 and 𝛼<1B.|α|≠|β| and |α|>1𝛼≠𝛽 and 𝛼>1C.|α|=|β| and |α|>1𝛼=𝛽 and 𝛼>1D.|α|≠|β| and |α|<1𝛼≠𝛽 and 𝛼<1PreviousClearMark for Review & NextNextInstructionsEnglishNot VisitedNot AnsweredAnsweredMarked for ReviewAnswered & Marked for review(will be considered for evaluation)MATHEMATICSSection-ISection-II6162636465666768697071727374757677787980

The roots of a quadratic equation ax^2 + bx + c = 0 are given by the formula:

α, β = [-b ± sqrt(b^2 - 4ac)] / 2a

The roots are imaginary if the discriminant (b^2 - 4ac) is less than zero.

Given that a, b, and c are all positive and a < b < c, it's clear that b^2 - 4ac will be less than zero, so the roots will indeed be imaginary.

The magnitude of the roots |α| and |β| will be equal because they are complex conjugates of each other. This is a property of quadratic equations: if the roots are complex, they will always come in conjugate pairs. So |α| = |β|.

The magnitude of the roots will be greater than 1 because the coefficients a, b, and c are all positive and a < b < c. This means that the roots will be further from the origin than 1 in the complex plane.

So, the correct answer is C. |α| = |β| and |α| > 1.