The graph of the equation $3 x^{2} + 4 x + 5$ = 0 intersects the x-axis at point(s).

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Solution

The correct option is A 0
The point at which the graph of a polynomial intersects the $X$ -axis is called a root of the corresponding equation.
A quadratic polynomial will intersect the $X$ -axis, if it has real roots.
The nature of the roots of a polynomial $a x^{2} + b x + c$ depends on its discriminant, $D$ = $b^{2} - 4 a c .$
Consider the equation $3 x^{2} + 4 x + 5 = 0.$
$⟹ D = b^{2} - 4 a c = 4^{2} - 4 (3) (5)$
$= - 44$
Since $D = - 44 < 0,$ the given equation has no real roots.
Hence, there will be no point of intersection of the polynomial with the $X$ -axis.

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3 x^{2} + 4 x + 5

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