Question

find the nature of roots x^2-25=0​

Answer 1

Answer:

x²-25=0

x²=25

x=√25

x=±5

D=b²-4ac

=0-4*1*(-25) =100

Roots are real and unequal:

rational roots.

Answer 2

Answer:

The roots of the equation are unequal(distinct) and rational.

Step-by-step explanation:

Given: The equation is$x^2-25=0$.

We have to find the nature of the roots$x^2-25=0$.

We are solving in the following way:

We have,

$x^2-25=0$

Comparing the given equation with the standard quadratic equation$a x^{2}+b x+c=0$,

We get,

$a=1, b=0, c=-25$

$\begin{array}{l}\therefore \Delta=b^{2}-4 a c \\=(0)^{2}-4(1)(-25) \\=0+100 \\=100 \\=(10)^{2}\end{array}$

Here, Δ>0 and is a perfect square. Also, a and b are rational.

Hence, the roots of the equation are unequal(distinct) and rational.