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4.2 Quadratic equations and inequations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.2 Quadratic equations and inequations1 Mark
MCQ
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 $(\lambda ,\mu )=$
  • ✓
    $(4, 4)$
  • B
    $(-4,4)$
  • C
    $(4, - 4)$
  • D
    $( - 4, - 4)$
✓

Answer

Correct option: A.
$(4, 4)$
a
(a) We have equal roots, therefore ${\lambda ^2} = 4\mu $.

Now second equation ${x^2} + \lambda x - 12 = 0$ has a root $2$,

so put $x = 2$==> $4 + 2\lambda - 12 = 0$==> $\lambda = 4$

Hence from ${\lambda ^2} = 4\mu $, we have $\mu = \frac{{16}}{4} = 4$

==> $(\lambda ,\mu ) = (4,4)$.

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