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The expression ax^2+2bx+c, where 'a' is ...

The expression `ax^2+2bx+c`, where 'a' is non-zero real number, has same sign as that of 'a' for every real value of x,then roots of quadratic equation `ax^2+ (b-c) x-2b-c -a-0` are: (a) real and equal (b) real and unequal (c) non-real having positive real part(d) non-real having negative real part

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Given expression, `ax^2+2bx+c` has the same sigh as that of `a`.
`:.` If `a gt 0`, then, `D gt 0`.
`b^2-4ac gt 0 => b^2 gt 4ac`.
`ax^2+(b-c)x - 2b - c-a = 0`
Here, `D = (b-c)^2 - 4a(-2b-c-a)`
`=>D = b^2+c^2-2bc +8ab+4ac+4a^2`
`=>D = 4a^2+b^2+c^2+8ab+4ac-2bc`
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