If α and β are the roots of the equation
2x(2x + 1) = 1, then β is equal to :

Solution

Maths sir · 3 steps

Get β from the sum of roots, then let the equation for α replace the leftover constant.

1. Standard form. Expanding gives 4x² + 2x - 1 = 0. So the sum of roots is α + β = -2/4 = -1/2, which means β = -1/2 - α.
2. Alpha is a root. Since α is a root, 4α² + 2α = 1. Dividing by 2 gives 1/2 = 2α² + α, so the constant 1/2 can be written in terms of α.

   β = -(2α² + α) - α = -2α² - 2α = -2α(α + 1)

3. So. β = -2α(α + 1), which is option (a).

The idea to keep. When one root must be written in terms of the other, start from the sum of roots. Then replace any leftover constant using the equation that the known root satisfies.

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