SATHEE: Theory of Equations 1 Question 28

Theory of Equations 1 Question 28

29. If $α$ and $β (α < β)$ are the roots of the equation $x^{2} + b x + c = 0$ , where $c < 0 < b$ , then

$(2000, 1 M)$

(a) $0 < α < β$

(b) $α < 0 < β < | α |$

(d) $α < 0 < | α | < β$

Show Answer

Answer:

Correct Answer: 29. (b)

Solution:

Given,

$c < 0 < b$

Since,

$α + β = - b$

and

$α β = c$

From Eq. (ii), $c < 0 \Rightarrow α β < 0$

$\Rightarrow$ Either $α$ is $- v e, β$ is - ve or $α$ is + ve, $β$ is - ve.

From Eq. (i), $b > 0 \Rightarrow - b < 0 \Rightarrow α + β < 0 \Rightarrow$ the sum is negative.

$\Rightarrow$ 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 $β$

$\Rightarrow α < 0 < β < | α |$

NOTE This question is not on the theory of interval in which root lie, which appears looking at first sight. It is new type and first time asked in the paper. It is important for future. The actual type is interval in which parameter lie.

Theory of Equations 1 Question 28

29. If $α$ and $β (α < β)$ are the roots of the equation $x^{2} + b x + c = 0$ , where $c < 0 < b$ , then

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Theory of Equations 1 Question 28

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

29. If $α$ and $β (α < β)$ are the roots of the equation $x^{2} + b x + c = 0$ , where $c < 0 < b$ , then