Question

Write the discriminant of $4x^2-20x+25=0$ and determine the nature of its root.

Answer 1

Step 1: Comparison with the standard form of the quadratic equation $a{x}^2+bx+c=0$

The given quadratic equation is $4x^2-20x+25=0$.

Here, $a=4,b=-20$ and $c=25$.

Step 2: Finding the discriminant

Using the formula for discriminant $\left(D\right)=b^2-4ac$ and substituting values of $a,b$ and $c$ we get,

$$\begin{gathered} D={(-20)}^2-4\left(4\right)\left(25\right) \\ ={(-20)}^2-\left(4^2\right)\left(5^2\right) \\ ={(-20)}^2-{\left[\right(4\left)\right(5\left)\right]}^2 \\ ={(-20)}^2-{\left(20\right)}^2 \\ =0 \end{gathered}$$

Step 3: Determining the nature of the roots of the equation

We know that the value of the discriminant decides the nature of the roots of the quadratic equation.

If $D>0$, then the quadratic equation has real and unequal roots.

If $D=0$, then the quadratic equation has real and equal roots.

If $D<0$, then the quadratic equation has no real roots.

For the given quadratic equation $D=0$. So, the equation has real and equal roots.

Therefore, the quadratic equation $4x^2-20x+25=0$ has real and equal roots.