Question

6.
x2 - 30x + 225 = 0 have
a) Real roots
b) No real roots
c) Real and Equal roots
d) Real and Distinct roots​

Answer 1

x² - 30x + 225 = 0 have Real and Equal roots

Given :

The equation x² - 30x + 225 = 0

To find :

x² - 30x + 225 = 0 have

a) Real roots

b) No real roots

c) Real and Equal roots

d) Real and Distinct roots

Solution :

Step 1 of 2 :

Find the roots of the equation

Here the given equation is x² - 30x + 225 = 0

This is a quadratic equation

Now ,

$\displaystyle \sf {x}^{2} - 30x + 225 = 0$

$\displaystyle \sf{ \implies }{x}^{2} - 2.x.15 + {15}^{2} = 0$

$\displaystyle \sf{ \implies } {(x - 15)}^{2} = 0$

$\displaystyle \sf{ \implies }x = 15 \: , \: 15$

So the roots of the quadratic equation are 15 , 15

Step 2 of 2 :

Find nature of the roots

The roots of the quadratic equation x² - 30x + 225 = 0 are 15 , 15

The roots are real

Also the roots are equal

Thus x² - 30x + 225 = 0 have real and equal roots

Hence the correct option is c) Real and Equal roots

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ find the equation that formed by increasing each root of 2x²-3x-1=0by 1

https://brainly.in/question/33063519

2. find the equation that formed by squaring each root of the equation x²+3x-2=0

https://brainly.in/question/33064705

#SPJ3

Answer 2

The correct option is c) Real and Equal roots.

The equation x^2 - 30x + 225 = 0 can be expressed as having real roots that are equal in value. This means that both solutions to the equation will yield the same result and that these solutions exist within the realm of real numbers.

One way to determine this is by factoring the equation, which results in (x - 15)^2 = 0. This shows that both roots of the equation are equal to 15, as the equation can be written as (x - 15)(x - 15) = 0.

Additionally, the solutions can also be found using the quadratic formula, which involves solving for the roots of the equation using a mathematical formula that takes into account the coefficients of the equation. The quadratic equation x2 - 30x + 225 = 0 has 15 and 15 roots.

Both of these methods lead to the conclusion that the equation has real and equal roots.

For more such questions on real roots: https://brainly.in/question/17396512

#SPJ3