The coefficients a, b and c of the quadratic equation, a x ^ 2 + bx...

a{x}^{2} + bx + c = 0$</p><p>$a, b, c \in { 1, 2, 3, 4, 5, 6 }$</p><p>$n ( s ) = 6 \times 6 \times 6 = 216$</p><p>For equal root$D = 0$</p><p>$⇒ {b}^{2} = 4ac$</p><p>Case I:$ac = 1$</p><p>\left(a, b, c\right) = \left(1, 2, 1\right)</p><p>Case II:$ac = 4$</p><p>\left(a, b, c\right) = \left(1, 4, 4\right)</p><p>or \left(4, 4, 1\right)</p><p>or \left(2, 4, 2\right)</p><p>Case-III:$ac = 9$</p><p>\left(a, b, c\right) = \left(3, 6, 3\right)</p><p>Required probability =\dfrac{5}{216}$