If the coefficients are rational numbers, then find the nature of the roots of the equation $x^{2} + 3 x - 2 = 0$

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Solution

Here $a = 1, b = 3, c = - 2$

$Δ = b^{2} - 4 a c = {(3)}^{2} - 4 \times 1 \times - 2 = 9 + 8 = 17 > 0$ (not a perfect square)

$∴$ the roots are irrational and conjugate to each other.

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