Question

Solve quadratic equation x^2-45x+324

Answer 1

hi mate,

Factoring x²-45x+324

x² - 36x - 9x - 324

Step-1 : Add up the first 2 terms, pulling out like factors :

x • (x-36)

Add up the last 2 terms, pulling out common factors :

9 • (x-36)

Step-2 : Add up the four terms of step 1 :

(x-9) • (x-36)

Which is the desired factorization

Final result :

(x - 9) • (x - 36)

take

x-9 = 0 and x -36 = 0

x = 9 and x = 36 are the roots of equation..

i hope it helps you.

Answer 2

Given

x²- 45x + 324

To Find

The roots of the quadratic equation

Solution

To find the roots of this quadratic equation we will start by factorizing the equation.

We will find two numbers whose product is 324.

The two numbers must also be such that the sum of both these numbers is negative 45.

When we use the factorizing method and factorize the number 324 we find the numbers 36 and 9 that suit our given situation.

Their sum is 45 and the product is 324.

x²- 45x + 324

x² - 36x - 9x + 324

Now let us group the first and later part of the equation

(x² - 36x) + (- 9x + 324)

Taking out the common multiples

x (x-36) - 9(x-36)

Again, taking out the common multiples

(x-36) x - 9

(x-36) (x-9)

Solving this equation we get

x-9 = 0

x = 9

and

x -36 = 0

x = 36

Therefore, 9 and 36 are the roots of equation.