Given quadratic function [tex]y = 2x^{2} +7x+6[/tex] intersects the x-axis two times.
What is quadratic function?
" Quadratic function is defined as the function which has variables with highest degree two."
According to the question,
Given quadratic function,
[tex]y = 2x^{2} +7x+6[/tex]
If quadratic function intersect x-axis value of [tex]y=0[/tex] we have,
[tex]2x^{2} +7x+6 =0\\\\\implies 2x^{2} + 4x+3x + 6=0\\ \\\implies 2x(x+2) + 3(x+2)=0\\\\\implies (2x+3) (x+2)=0\\\\\implies 2x+3 =0 \ or \ x+2=0\\\\\implies x = \frac{-3}{2} \ or \ x =-2\\\\\implies x = -1.5 \ or \ x =-2[/tex]
As shown in graph , quadratic function intersect x-axis at two points [tex](-2,0)[/tex] and [tex](-1.5,0)[/tex].
Hence, given quadratic function [tex]y = 2x^{2} +7x+6[/tex] intersects the x-axis two times.
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