If α, β ∈ R are such that 1 - 2i (here i² = -1) is a root of z² + αz + β = 0, then (α - β) is equal to :

Solution

Maths sir · 3 steps

Real coefficients mean 1+2i is the other root. Then just use sum and product of roots.

1. Conjugate root. Since α and β are real, complex roots come in conjugate pairs. So the two roots are 1-2i and 1+2i.
2. Sum of roots. For z²+α z+β=0, the sum of roots is -α. Here (1-2i)+(1+2i)=2, so -α=2 and α=-2.

   β=(1-2i)(1+2i)=1-4i²=1+4=5

3. So. α-β=-2-5=-7, which is option (a).

The idea to keep. A real quadratic with root a+bi also has root a-bi. The quadratic is z²-2az+(a²+b²)=0, so read the coefficients straight off.

Answer from the NTA final answer key. Solution by PrepWiser.