Question:
Let α and β ( α < β ) be the roots of the equation x2 + bx + c = 0 , where b > 0 and c < 0 . Consider the followingnI. β < -α nII. β < |α| nWhich of the above statement(s) is/are correct?
Let α and β ( α < β ) be the roots of the equation x2 + bx + c = 0 , where b > 0 and c < 0 . Consider the followingnI. β < -α nII. β < |α| nWhich of the above statement(s) is/are correct?
Options:
- Only II
- Only I
- Neither I nor II
- Both I and II
- Only II
- Only I
- Neither I nor II
- Both I and II
Correct Answer: d)
Explanation:
‘ Gi√en, a and 3 are the r∞ts of equation x2 + bx + ¢ = 0.
‘ sa+pf=—-bandaf=c
Asb>0andc<0
‘ So,a+B<0=p<—-a
‘ and af <0
1 Also, gi√en that a < 8
‘ =a<0andf>0
‘ a+B<0=B<—a..(i
.. Statement I is correct. 1
‘ Asa <0and —a>f
= la > 8
1 .”. Statement II is correct.
‘ Gi√en, a and 3 are the r∞ts of equation x2 + bx + ¢ = 0.
‘ sa+pf=—-bandaf=c
Asb>0andc<0
‘ So,a+B<0=p<—-a
‘ and af <0
1 Also, gi√en that a < 8
‘ =a<0andf>0
‘ a+B<0=B<—a..(i
.. Statement I is correct. 1
‘ Asa <0and —a>f
= la > 8
1 .”. Statement II is correct.