x2 + 6x + 19 > 0
Explanation:
In a quadratic expression ax2 + bx + c, if a > 0 and (b2 – 4ac) < 0, then the expression is always positive for all real values of x.
Here, b2 – 4ac = 36 – 4 × 1 × 19 = - 40 < 0 and a > 0
∴ x2 + 6x + 19 is always positive for all possible values of x.
Hence, option (a).
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