Question

Which of the following equations has no real roots
a) X² - 4X + 3 ROOT 2 =0b) X² - 4X - 3 ROOT 2 =0
c) X² + 4X - 3 ROOT 2 =0 d) 3X²+ 4 Root 3X + 4=0

Answer 1

Answer :

We know : Where b² - 4ac < 0 than our equation has no real roots .

For :

a ) x² - 4 x + 3 $\sqrt{2}$ , Here a = 1 , b = - 4 and c = 3 $\sqrt{2}$ , So
$$\begin{gathered} {\left(-4\right)}^2-4\times 1\times 3\sqrt{2} \\ \Rightarrow 16-12\sqrt{2} \\ \Rightarrow 16-12\times 1.414(\mathrm{We}\mathrm{know}\sqrt{2}=1.414) \\ \Rightarrow 16-16.968 \\ \Rightarrow -0.968 \\ \mathrm{So}, \\ \mathbf{-}\mathbf{}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{968}\mathbf{}\mathbf{}\mathbf{<}\mathbf{}\mathbf{0}\mathbf{} \end{gathered}$$
We can say x² - 4 x + 3 $\sqrt{2}$ has no real roots .

Option ( A ) ( Ans )