In the quadratic equation

We can find the nature of its roots by using the discriminant

We have 3 cases

#a)
For the quadratic equation

a = -2
b = 16
c = -35
Let us find the discriminant to find the nature of the roots

Since the value is negative, then we will use the 3rd case above
The equation has NO Real roots
The quadratic function has NO real roots, it will have imaginary roots
#b
For the quadratic equation

Since it has only one x-intercept
That means it has only ONE real root
Then we will use the 2nd case above

Since:
a = 9
b = k
c = 16
Then

Add 576 to each side

Take a square root for each side
![\begin{gathered} \sqrt[]{k^2}=\pm\sqrt[]{576} \\ k=\pm24 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/bxnkwno2k0r80txbk6j169ppcvl8t0xkza.png)
The values of k are -24 and 24