Question

State whether the following quadratic equations have two distinct real roots. Justify your answer.

$x^2-3x+4=0$

Answer 1

Nature of roots.

The discriminants of a quadratic equation $a{x}^2+bx+c=0$ is given by:

$D=b^2-4ac$

• If $D>0$, the roots are distinct and real.
• If $D=0$, the roots are equal and real.
• If $D<0$, the roots will be imaginary.

The discriminant of the given quadratic equation $x^2-3x+4=0$is computed as:

$$\begin{gathered} \therefore D={(-3)}^2-4·1·4 \\ \Rightarrow D=9-16 \\ \Rightarrow D=-7 \\ \Rightarrow D<0 \end{gathered}$$

Since , the discriminant is less than zero.

Hence, the roots are imaginary.