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If a ,b ,c in R^+a n d2b=a+c , then che...

If `a ,b ,c in R^+a n d2b=a+c ,` then check the nature of roots of equation `a x^2+2b x+c=0.`

Text Solution

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The correct Answer is:
Roots are real and distinct.
Given equation is `ax^(2) + 2bx + c= 0`. Hence,
`D = 4b^(2) - 4ac`
`=(a + c)^(2) - 4ac`
`= (a - c)^(2) gt 0`
Thus, the roots are real and distinct.
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