Question

If α and β (α<β) are the roots of the equation x² + bx + c = 0, where c < 0 < b, then

• A. 0 <α<β
• B. α< 0 < β< |α|
• C. α<β< 0
• D. α< 0 < |α| <β

Answer 1

Answer: (B)

α< 0 < β< |α|

Answer 2

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

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

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

⇒ modules of nengative quantity is > modulus of positive

quantity but α < β is given.

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