If `a x^2+b x+c=0,a ,b ,c in R` has no real zeros, and if `c<0` , then which of the following is true? `a<0` `a+b+c >0` `a >0`

Explanation

Given that `a x^2+b x+c=0,a ,b ,c in R` has no real zeros.

`implies b^2 – 4ac < 0`

`b^2 < 4ac`

`4ac > b^2`

Since `b in R`, then `b^2 ge 0`.

`4ac > 0`

`implies` a and c both have same signs.

Since `c < 0`, then `a < 0`.