Answer:
(a)Two real solutions.
(b)No real solution
Explanation:
The discriminant of a standard quadratic function y=ax²+bx+c is obtained by using the formula:
[tex]D=b^2-4ac[/tex]Part A
[tex]\begin{gathered} x^2+7x+10=0 \\ a=1,b=7,c=10 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} D=7^2-4(1)(10) \\ =49-40 \\ =9 \\ D>0 \end{gathered}[/tex]Since D is greater than 0, the quadratic equation has two distinct real solutions.
Part B
[tex]\begin{gathered} 4x^2-3x+4=0 \\ a=4,b=-3,c=4 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} D=(-3)^2-4(4\times4) \\ =9-64 \\ =-55 \\ D<0 \end{gathered}[/tex]Since D is less than 0, the quadratic equation has No real solution.
