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STD 11 - 4.2 Quadratic equations and inequations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.2 Quadratic equations and inequations4 Marks
MCQ
Two real numbers $\alpha$ and $\beta $ are such that $\alpha  + \beta  = 3$ and $\left| {\alpha  - \beta } \right| = 4$, then $\alpha$  and  $\beta $  are the roots of the quadratic equation
  • ✓
    $4x^2-12x-7=0$
  • B
    $4x^2-12x+7=0$
  • C
    $4x^2-12x+25=0$
  • D
    none of these
✓

Answer

Correct option: A.
$4x^2-12x-7=0$
a
$\alpha+\beta=3$

also $(\alpha-\beta)^{2}=(\alpha+\beta)^{2}-4 \alpha \beta$

$\Rightarrow \quad \alpha \beta=-\frac{7}{4}$

required quadratic equation is

$  x^{2}-x(3)-\frac{7}{4}=0 $

$ \Rightarrow  4 x^{2}-12 x-7=0$

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