InterviewSolution
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InterviewSolution
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Let `a gt 0, b gt 0 and c lt0.` Then, both the roots of the equation `ax^(2) +bx+c=0`A. are real and nagativeB. have negative real partsC. have positive real partsD. None of the above |
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Answer» Correct Answer - B Since, `a, b, c gt 0 an ax^(2)+bx+c=0` `impliesx=(-b)/(2a)+-(sqrt(b^(2)-4ac))/(2a)` Case I When `b^(2)-4acgt0` `impliesx=(-b)/(2a)-(sqrt(b^(2)-4ac))/(2a)and (-b)/(2a)+(sqrt(b^(2)-4ac))/(2a)` both roots, are negative. Case II When `b^(2)-4ac=0` `impliesx(-b)/(2a),` i.e. both roots are equal and negative Case III When `b^(2)-4ac lt0` `impliesx=(-b)/(2a)+-i(sqrt(4ac-b^(2)))/(2a)` have negative real part. `therefore` Form above discussion, both roots have negative real parts |
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