MCQ
$2\text{x}^{2}+5\sqrt{3} \text{ x}+6 = 0$ have :
- ✓Real and Distinct roots
- BReal and equal root
- CNo Real roots
- DReal roots
✓
Answer
Correct option: A.
Real and Distinct roots
Comparing the given equation to the below equation
$\text{ax}^{2} + \text{bx}+\text{c} = 0$
$\text{a} = 2,\text{b} = 5\sqrt{3},\text{c} = 6$
$\text{D} = \text{b}^{2}-\text{4ac}$
$\text{D} = (5\sqrt{3})^{2} - 4\times2\times6$
$\text{D} = 75 - 48$
$\text{D} = 27$
$\text{D}>0$
If $b^2-4 a c>0,$
then the equation has real and distinct roots.
$\text{ax}^{2} + \text{bx}+\text{c} = 0$
$\text{a} = 2,\text{b} = 5\sqrt{3},\text{c} = 6$
$\text{D} = \text{b}^{2}-\text{4ac}$
$\text{D} = (5\sqrt{3})^{2} - 4\times2\times6$
$\text{D} = 75 - 48$
$\text{D} = 27$
$\text{D}>0$
If $b^2-4 a c>0,$
then the equation has real and distinct roots.
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