we know that
Use the value of the discriminant to determine the nature of the solutions to the quadratic equation.
so
The discriminant is equal to
[tex]D=b^2-4ac[/tex]
Part 23
we have
[tex]\begin{gathered} 49c^2+4=-28c \\ \text{equate to zero the quadratic equation} \\ 49c^2+28c+4=0 \\ a=49 \\ b=28 \\ c=4 \\ \text{substitute in the equation of discriminant} \\ D=(28^2)-4(49)(4) \\ D=784-784 \\ D=0 \end{gathered}[/tex]
that means -----> the roots are equal and real.
part 24
we have
[tex]\begin{gathered} (3x+1)^2=5x-1 \\ 9x^2+6x+1=5x-1 \\ 9x^2+6x-5x+1+1=0 \\ 9x^2+x+2=0 \\ a=9 \\ b=1 \\ c=2 \\ \text{substitute} \\ D=(1^2)-4(9)(2) \\ D=1-72 \\ D=-71 \\ \end{gathered}[/tex]
that means -----> The discriminant is negative, so the equation has two non-real solutions.
Part 26
we have
[tex]\begin{gathered} 5z^2+2z-4=0 \\ a=5 \\ b=2 \\ c=-4 \\ \text{substitute} \\ D=(2^2)-4(5)(-4) \\ D=4+80 \\ D=84 \end{gathered}[/tex]
that means -----> The discriminant is positive, so the equation has two distinct real solutions.
