If the equation x^2 + lambda x + mu = 0 has e | vedclass

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Question

(A) Given that the equation $x^2 + \lambda x + \mu = 0$ has equal roots,the discriminant must be zero: $\lambda^2 - 4\mu = 0$,which implies $\lambda^2

Vedclass · Accepted Answer

$(4, 4)$

Vedclass · Answer

(A) Given that the equation $x^2 + \lambda x + \mu = 0$ has equal roots,the discriminant must be zero: $\lambda^2 - 4\mu = 0$,which implies $\lambda^2 = 4\mu$.For the second equation $x^2 + \lambda x - 12 = 0$,$x = 2$ is a root.Substituting $x = 2$ into the equation: $2^2 + \lambda(2) - 12 = 0$.$4 + 2\lambda - 12 = 0$.$2\lambda = 8$,so $\lambda = 4$.Now,substitute $\lambda = 4$ into the first relation $\lambda^2 = 4\mu$:$4^2 = 4\mu$.$16 = 4\mu$,so $\mu = 4$.Thus,$(\lambda, \mu) = (4, 4)$.

If the equation $x^2 + \lambda x + \mu = 0$ has equal roots and one root of the equation $x^2 + \lambda x - 12 = 0$ is $2$,then $(\lambda, \mu) = $

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