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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
Two students while solving a quadratic equation in $x$, one copied the constant term incorrectly and got the roots $3$ and $2$. The other copied the constant term and coefficient of ${x^2}$ correctly as $-6$ and $1$ respectively. The correct roots are
  • A
    $3, -2$
  • B
    $ - 3,\,2$
  • C
    $-6, -1$
  • ✓
    $6, - 1$
✓

Answer

Correct option: D.
$6, - 1$
d
(d) Let the correct equation be $a{x^2} + bx + c = 0$ and the correct roots $\alpha $ and$\beta $.

Taking $c$ wrong, the roots are $3$ and $2$.

? $\alpha + \beta = 3 + 2 = 5$ .....$(i)$

Also $a = 1$ and $c = - 6$

? $\alpha \beta = c/a = - 6$.....$(ii)$

Solving $(i)$ and $(ii)$, the correct roots are $6$ and $-1$.

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