Question

Identify the zeroes of the given polynomial
$p\left(z\right)=4z^2-15z\pi -4{\pi }^2$

• A. $4\pi ,-\frac{\pi }{4}$
• B. $-4\pi ,\frac{\pi }{4}$
• C. $4\pi ,\frac{\pi }{4}$
• D. $-4\pi ,-\frac{\pi }{4}$

Answer 1

Answer: (A)

$4\pi ,-\frac{\pi }{4}$

Given $P\left(z\right)=4z^2-15\pi z-4{\pi }^2$

To find out its roots, we have to equate it to zero

$4z^2-15\pi z-4{\pi }^2=0$

$4z^2-16\pi z+\pi z-4{\pi }^2=0$

$4z(z-4\pi )+\pi (z-4\pi )=0$

$(4z+\pi )(z-4\pi )=0$

$z=4\pi ,-\frac{\pi }{4}$