Question

Which of the following equations has no solution for $a$ ?

• A. $a^2-6a+7=0$
• B. $a^2+6a-7=0$
• C. $a^2+4a+3=0$
• D. $a^2-4a+3=0$
• E. $a^2-4a+5=0$

Answer 1

The correct option is E $a^2-4a+5=0$

You can determine which of the equations has no solution by determining which equation has a negative discriminant:

(A) $b^2-4ac={(-6)}^2-4\left(1\right)\left(7\right)=36-28=8$

(B) $b^2-4ac={\left(6\right)}^2-4\left(1\right)(-7)=36+28=64$

(C) $b^2-4ac={\left(4\right)}^2-4\left(1\right)\left(3\right)=16-12=4$

(D) $b^2-4ac={(-4)}^2-4\left(1\right)\left(3\right)=16-12=4$

(E) $b^2-4ac={(-4)}^2-4\left(1\right)\left(5\right)=16-20=-4$