Question

5z² – 3z – 2 = 0

Answer 1

Given: 5z² – 3z – 2 = 0
On splitting the middle term –3z as 2z – 5z, we get:
5z² + 2z – 5z – 2 = 0
=> z(5z + 2) – 1(5z + 2) = 0
=> (5z + 2) (z – 1) = 0
We know that if the product of two numbers is zero, then at least one of them must be zero.
Thus, 5z + 2 = 0 or z – 1 = 0
=> z = –$\frac{2}{5}$ or z = 1
Therefore, the solution of the given equation is z = –$\frac{2}{5}$ ,1