Question

solve this
x square+24x+80​

Answer 1

Step-by-step explanation:

1.1 Factoring x2-24x+80

The first term is, x2 its coefficient is 1 .

The middle term is, -24x its coefficient is -24 .

The last term, "the constant", is +80

Step-1 : Multiply the coefficient of the first term by the constant 1 • 80 = 80

Step-2 : Find two factors of 80 whose sum equals the coefficient of the middle term, which is -24 .

-80 + -1 = -81

-40 + -2 = -42

-20 + -4 = -24 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -4

x2 - 20x - 4x - 80

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-20)

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

4 • (x-20)

Step-5 : Add up the four terms of step 4 :

(x-4) • (x-20)

Which is the desired factorization

Answer 2

Method 1 to solve :-

By using factorisation

p(x) = x² + 24x + 80

Putting p(x) = 0

→ x² + 24x + 80 = 0

Splitting the middle term

→ x² + 20x + 4x + 80 = 0

Taking common

→ x(x + 20) + 4(x + 20) = 0

→ (x + 20)(x + 4) = 0

Now , here either x + 20 = 0 or x + 4 = 0. So , by simplifying x = - 20 or - 4

Method 2 to solve :-

By Using quadratic formula

x = - b±√b² - 4ac/2a

Where

• b → coefficient of x = 24
• a → coefficient of x² = 1
• c → constant term = 80

Substituting the values we have

→ x = - 24 ±√24² - 4(1)(80)/2(1)

→ x = - 24 ±√576 - 320/2

→ x = - 24 ±√256/2

→ x = - 24 + 16/2 or -24 - 16/2

→ x = - 8/2 or - 40/2

→ x = - 4 or - 20

Hence , x = - 4 or -20 in both the methods.