What factors of 72 add to get you 17

Question

x^2+17x+72

Answer 1

 Should solve it without using quadratic formula:

  

   X² +  bX + C

 

   X²  +bX + C = ( X + m ) ( X +n)

 

    Such that  m+ n = 17   and mn = 72 in this case

 

      The answer is m=9  m = 8, the answer is 72= 8*9 , factors of 8, 9 whose sum is 17 is the answer 

 

   X² + 17x + 72 = ( X +9 ) ( X+8)

 

     

Answer 2

Here is formula, which can help you

ax² + bx + c = a(x - x₁)(x - x₂)
x₁ and x₂ are roots of quadratic equation
ax² + bx + c = 0
x₁₂ = [- b ± √(b² - 4ac)] / 2a
D = b² - 4ac 
If D > 0 , there are two real roots.
If D = 0 , there is only one real root.
if D < 0 , the quadratic equation does not have real roots and cannot be factorized in the set of real numbers.

x² + 17x + 72 =
a = 1  b = 17  c = 72
D = 17² - 4 * 1 * 72 = 1

x₁₂ = ( - 17 ± √1) / 2

x₁ = ( - 17 + 1) / 2 = - 8
x₂ = (-17 - 1) / 2 = - 9

x² + 17x + 72 = [x - ( - 8)] * [x - (- 9)] = (x + 8)(x + 9) 

Answer 3

yOU HAVE TO FIND 2 NUMBERS THAT ADDED GIVE A REASOULT 17 AND MULTIPLIED 72 SO, THIS NUMBERS ARE 9 AND 8 BECAUSE 9+8 17 AND 9*8=72

 

ok your final answer is (x+9) (x+8)