Question

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

• A. 0.0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A 0.0

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 $a{x}^2+bx+c$ depends on its discriminant, $D$ = $b^2-4ac.$
Consider the equation $3x^2+4x+5=0.$
$⟹D=b^2-4ac=4^2-4\left(3\right)\left(5\right)$
$=-44$
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.