The number of roots common between the two equations x^3 + 3x^2 + 4x + 5 = 0

• Quant Quadratic

The number of roots common between the two equations x³ + 3x² + 4x + 5 = 0 and x³ + 2x² + 7x + 3 = 0 is

1. 0
2. 1
3. 2
4. 3

Answer

Let α is the common root.

α³ + 3α² + 4α + 5 = 0

α³ + 2α² + 7α + 3 = 0

Subtracting one equation from another,

α² - 3α + 2 = 0

α = 2; α = 1

But the above values of α do not satisfy any of the equations. Thus, no root is common.

The correct option is A.