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Maths Trigonometrical Equations and in Equations, Properties of Triangles, Height and Distance Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If α α and β β ( α α < β β ) are the roots of the equation x 2 + bx + c = 0, where c < 0 < b, then

0 < α α < β β

α α < 0 < β β < | α α |

α α < β β < 0

α α < 0 < | α α | < β β

Text Solution

Verified by Experts

The correct answer is:

Given c < 0 < b and α α + β β = - b α α β β = c

from (2), c < 0 ⇒ ⇒ α α β β < 0 ⇒ ⇒ either α α is –ve or β β is –ve and second quantity is positive.

from (1), b > 0 ⇒ ⇒ - b < 0 ⇒ ⇒ α α + β β < 0 ⇒ ⇒ the sum is negative

⇒ ⇒ modules of nengative quantity is > modulus of positive

quantity but α α < β β is given.

Therefore, it is clear that α α is negative and β β is positive and modulus of α α is greater than modulus of β β ⇒ ⇒ α α < 0 β β < | α α |

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