Question

z – = 4z + 5

Answer 1

Given: z – $\frac{7}{z}$ = 4z + 5
On multiplying both sides by z, we get:
z² – 7 = 4z² + 5z
On transposing all the terms of the right-hand side to the left-hand side, we get:
z² – 7 – 4z² – 5z = 0
$\Rightarrow$ – 3z² – 5z – 7 = 0
On comparing this equation with the general form of the quadratic equation az² + bz + c = 0, we get:
a = –3, b = –5 and c = –7, which are real numbers and a $\ne$ 0.
Thus, the given equation is a quadratic equation in the variable z.