2. Comment on the nature of the roots of the equation : 4×2 + 5x + 2 = 0​

2 thoughts on “<br />2. Comment on the nature of the roots of the equation : 4×2 + 5x + 2 = 0​”

1. Answer :

   • d < 0 then it has no real roots

   Given :

   • 4x² + 5x + 2 = 0

   To find :

   • Nature of the roots of the equation

   Solution :

   》4x² + 5x + 2 = 0

   As we know that

   • D = b² – 4ac

   Where ,

   • a is 4
   • b is 5
   • c is 2

   》D = b² – 4ac

   》D = (5)² – 4(4)(2)

   》D = 25 – 32

   》D = – 7

   Verification :

   • D = b² – 4ac

   where , a is 4 , b is 5 , c is 2 and d is 7

   》 D = b² – 4ac

   》-7 = (5)² – 4(4)(2)

   》-7 = 25 – 32

   》-7 = -7

   Hence verified

   Hence, d < 0 then it has no real roots and unique

   Reply

2. Given :

   • [tex]\sf{4x}^{2}\:{+\:5x\:+\:2\:=\:0}[/tex]

   Find :

   • Nature of the roots of the equation.

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex]

   [tex]{ }[/tex]

   We Know that :

   • [tex]\sf{\red{D\:=\:b}^{\red 2}\:{\red -\:\red 4 \red a \red c}}[/tex]

   [tex]{ }[/tex]

   Where,

   • a = 4
   • b = 5
   • c = 2

   [tex]{ }[/tex]

   Now, putting the value in formula,

   • [tex]\sf{\pink{D\:=\:b}^{\pink 2}\:{\pink -\:\pink 4 \pink a \pink c}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:{\dashrightarrow\:\sf{D\:=\:5}^{2}\:{-\:4\:(4)\:(2)}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:{\dashrightarrow\:\sf{D\:=\:25\:-\:32}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:{\dashrightarrow\:\sf{D\:=\:-7}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\therefore\:{\underline{\sf{Hence,\:d\:<\:0\:then\:it\:has\:{\textsf{\textbf{no\:real\:roots\:and\:unique. }}}}}}.[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex]

   [tex]{ }[/tex]

   [tex]\:\:{\underline{\bold{\purple{\sf{V\:E\:R\:I\:F\:I\:C\:A\:T\:I\:O\:N\::}}}}}[/tex]

   [tex]{ }[/tex]

   • [tex]\sf{\pink{D\:=\:b}^{\pink 2}\:{\pink -\:\pink 4 \pink a \pink c}}[/tex]

   [tex]{ }[/tex]

   ★ So, know we know the value of D is –7.

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:\leadsto\:{\sf{-7\:=\:(5)}^{2}\:{-\:4\:(4)\:(2)}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:\leadsto\:{\sf{-7\:=\:25\:-\:32}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:\leadsto\:{\sf{-7\:=\:-7}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\underline{\textsf{\textbf{Hence\:Verified!!}}}}[/tex]

   [tex]{ }[/tex]

   [tex]\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━[/tex]

   [tex]{ }[/tex]

   Reply