Question

Which of the following equation ha no real root.
a› x²+ 4x - 3 √ 2 = 0
b› x²- 4x + 3 √ 2 = 0
c›x²-4x - 3 √ 2 = 0
d x²+ 4x + 3 √ 2 = 0​

Answer 1

Answer:

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Answer 2

Formula Used :

$\large\implies \tt D= {b}^{2} - 4ac \\ \\ \tt D> 0 \: \: \: \: \: \: 2 \: real \: root \\ \\ \tt D = 0\: \: \: \: \: \: 1 \: real \: root \\ \\ \tt D < 0\: \: \: \: \: \:2\: complex \: root$

Solution :

Case 1

$\tt D = {4}^{2} - 4 \times 1 \times ( - 3 \sqrt{2} ) \\ \\\tt D = 16+ 12 \sqrt{2} \\ \\\tt d =33$

Case 2

$\tt D = {( - 4)}^{2} - 4 \times 1 \times 3 \sqrt{2}\\ \\\tt D = 16 -12 \sqrt{2} \\ \\\tt D = - 1$

Case 3

$D = {( - 4)}^{2} - 4 \times 1 \times ( - 3 \sqrt{2} ) \\ \\\tt D = 16 + 12 \sqrt{2} \\ \\\tt D = 33$

Case 4

$\tt D = {4}^{2} - 4 \times 1 \times 3 \sqrt{2} \\ \\\tt D = 16 - 12 \sqrt{3} \\ \\\tt D = - 1$

Option 2 and 3 have no real root