[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's use the discriminant method, we have to find discriminant of the given quadratic function, if discriminant is greater than 0, then it has two intercepts, if it is equal to 0, then it has 1 intercepts and if it is smaller than 0, then it has no x intercepts.
[tex]\qquad \sf \dashrightarrow \:D = {b}^{2} - 4ac[/tex]
where, a, b and c are coefficients of x², x and constant term. D = discriminant
[tex]\qquad \sf \dashrightarrow \:D = {( - 30)}^{2} - 4(22 \times 1)[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 900 - 4(22 )[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 900 - 88[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 812[/tex]
Discriminant is greater than 0, hence it has two x - intercepts.
