Question

Which of the following equations has no real roots?

• A. $x^2+4x+3\sqrt{2}=0$
• B. $x^2+4x-3\sqrt{2}=0$
• C. $x^2+5x+3\sqrt{2}=0$
• D. $3x^2+4\sqrt{3}x+4=0$

Answer 1

The correct option is A $x^2+4x+3\sqrt{2}=0$

The quadratic equation $a{x}^2+bx+c=0$ has no real roots only when discriminant $D<0$

$D=b^2-4ac<0$

A) $x^2+4x+3\sqrt{2}=0$

Here,

$D=(4{)}^2-4\times 3\sqrt{2}$

$=16-16.97<0$

B) $x^2+4x-3\sqrt{2}=0$

Here,

$D=(4{)}^2-4\times (-3\sqrt{2})$

$=16+16.97>0$

C) $x^2+5x+3\sqrt{2}=0$

Here,

$D=(5{)}^2-4\times (3\sqrt{2})$

$=25-16.97>0$

D) $3x^2+4\sqrt{3}x+4=0$

Here,

$D=(4\sqrt{3}{)}^2-4\times 3\times 4$

$=48-48=0$

Hence, option A.