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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For the equation $x^2 + \lambda x + \mu = 0$ to have equal roots,the discriminant must be zero,i.e.,$D = \lambda^2 - 4\mu = 0$,which implies $\lam

Vedclass · Accepted Answer

$(4, 4)$

Vedclass · Answer

(A) For the equation $x^2 + \lambda x + \mu = 0$ to have equal roots,the discriminant must be zero,i.e.,$D = \lambda^2 - 4\mu = 0$,which implies $\lambda^2 = 4\mu$.Given that $x = 2$ is a root of the equation $x^2 + \lambda x - 12 = 0$,we substitute $x = 2$ into the equation:$2^2 + \lambda(2) - 12 = 0$$4 + 2\lambda - 12 = 0$$2\lambda - 8 = 0$$2\lambda = 8$$\lambda = 4$Now,substitute $\lambda = 4$ into the relation $\lambda^2 = 4\mu$:$4^2 = 4\mu$$16 = 4\mu$$\mu = 4$Therefore,$(\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) = $

Similar Questions

If $x = 2^{1/3} - 2^{-1/3}$,find the value of $2x^3 + 6x$.

If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$,then the other roots are

Determine $p$ such that the equation $x^{2}+5px+16=0$ has no real roots.

The set of all real values of $\lambda$ for which the quadratic equation $(\lambda^{2}+1) x^{2}-4 \lambda x+2=0$ has exactly one root in the interval $(0,1)$ is

Solve the given equations and choose the correct option.
$I.$ $x = \sqrt{(36)^{1/2} \times (1296)^{1/4}}$
$II.$ $2y + 3z = 33$
$III.$ $6y + 5z = 71$

Vedclass Test Series

Exam Paper Generator

Online Exam Module