If the equation ax^(2) + bx + c = 0, a,b...

If the equation `ax^(2) + bx + c = 0, a,b, c, in` R have non -real
roots, then

A

`c(a - b +c)gt 0`

B

`c (a + b + c) gt 0 `

C

`c( 4a - 2b + c) gt0 `

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

1,2,3

Since the roots if ` ax^(2) + bx + c = 0 ` are nonreal , so `f(x) = ax^(2) + bx + c `
Will have same sign for every value of x. Hence,
` f(0) = c. f(1) = a + b + c, f (-1) = a - b +c`
` f(-2) = 4 a - 2b + c `
`rArr c (a +b + c) gt 0, c(a - b + c) gt 0 , c (4a - 2b + c ) gt 0 ` .

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