Quadratic EquationMedium
Question
If α and β (α < β) are the roots of the equation x2 + bx + c = 0 where c < 0 < b , then
Options
A.0 < α < β
B.α < 0 < β < α
C.α < β < 0
D.α < 0 |α| < β
Solution
Given, c < 0 < b
Since α + β = - b ......(i)
and αβ = c .......(ii)
From Eq. (ii), c < 0 ⇒ αβ < 0
⇒ Either α is - ve OR α is + ve, β is - ve.
From Eq. (i), b > 0 ⇒ - b < 0 ⇒ α + β < 0 ⇒ the sum is negative.
Modulus of negative 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|
Note. This quesition is not on the theory of Interval in which root lie, which appears looking at first, It is new type and first time asked in the paper. It is Important. gor future. The actual type is Interval in which parameter lie.
Since α + β = - b ......(i)
and αβ = c .......(ii)
From Eq. (ii), c < 0 ⇒ αβ < 0
⇒ Either α is - ve OR α is + ve, β is - ve.
From Eq. (i), b > 0 ⇒ - b < 0 ⇒ α + β < 0 ⇒ the sum is negative.
Modulus of negative 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|
Note. This quesition is not on the theory of Interval in which root lie, which appears looking at first, It is new type and first time asked in the paper. It is Important. gor future. The actual type is Interval in which parameter lie.
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