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If a+b+c=0 then check the nature of root...

If `a+b+c=0` then check the nature of roots of the equation `4a x^2+3b x+2c=0w h e r ea ,b ,c in Rdot`

Text Solution

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The correct Answer is:
Roots are real and distinct.
For the given equation `4ax^(2) + 3bx + 2c = 0`, we have
`D = (3b)^(2) - 4 (4a) (2c)`
= `9b^(2) - 32 ac`
= `9 (-a -c)^(2) - 32 ax `
`= 9a^(2) - 14 ac + 9c^(2)`
` = 9c^(2) (((a)/(c))^(2) - (14)/(9) (a)/(c) + 1)`
` = 9 (((a)/(c)-(7)/(9))^(2) - (48)/(81) + 1)`
Which is always positive. Hence, the roots are real and distinct
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