Question

2. Comment on the nature of the roots of the equation : 4x2 + 5x + 2 = 0​

Answer 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

Answer 2

Given :

• $\sf{4x}^{2}\:{+\:5x\:+\:2\:=\:0}$

Find :

• Nature of the roots of the equation.

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We Know that :

• $\sf{\red{D\:=\:b}^{\red 2}\:{\red -\:\red 4 \red a \red c}}$

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Where,

• a = 4
• b = 5
• c = 2

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Now, putting the value in formula,

• $\sf{\pink{D\:=\:b}^{\pink 2}\:{\pink -\:\pink 4 \pink a \pink c}}$

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$\:\:\:\:\:\:{\dashrightarrow\:\sf{D\:=\:5}^{2}\:{-\:4\:(4)\:(2)}}$

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$\:\:\:\:\:\:{\dashrightarrow\:\sf{D\:=\:25\:-\:32}}$

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$\:\:\:\:\:\:{\dashrightarrow\:\sf{D\:=\:-7}}$

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

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$\:\:{\underline{\bold{\purple{\sf{V\:E\:R\:I\:F\:I\:C\:A\:T\:I\:O\:N\::}}}}}$

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• $\sf{\pink{D\:=\:b}^{\pink 2}\:{\pink -\:\pink 4 \pink a \pink c}}$

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

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$\:\:\:\:\:\:\leadsto\:{\sf{-7\:=\:(5)}^{2}\:{-\:4\:(4)\:(2)}}$

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$\:\:\:\:\:\:\leadsto\:{\sf{-7\:=\:25\:-\:32}}$

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$\:\:\:\:\:\:\leadsto\:{\sf{-7\:=\:-7}}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\underline{\textsf{\textbf{Hence\:Verified!!}}}}$

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