Answer:
20*21 = 420 and (-21)*(-20) = 420
Any constant less or equal than 0.25
Step-by-step explanation:
The product of two consecutive integers is 420 can be expressed mathematically as follows:
x*(x+1) = 420
After applying distributive property and subtracting 420 at both sides, we get:
x^2 + x - 420 = 0
In order to factorise, we use the quadratic equation as follows:
[tex]x = \frac{-b \pm \sqrt{b^2-4(a)(c)}}{2(a)} [/tex]
[tex]x = \frac{-1 \pm \sqrt{1^2-4(1)(-420)}}{2(1)} [/tex]
[tex]x = \frac{-1 \pm \sqrt{1681}}{2} [/tex]
[tex]x = \frac{-1 \pm 41}{2} [/tex]
[tex]x_1 = \frac{-1 + 41}{2} [/tex]
[tex]x_1 = 20 [/tex]
[tex]x_2 = \frac{-1 - 41}{2} [/tex]
[tex]x_2 = -21 [/tex]
Then, 20*21 = 420 and (-21)*(-20) = 420
A quadratic equation with the standard form has a solution to the equation: a*x^2 + b*x + c = 0 if its discriminant is greater or equal than zero. Mathematically:
b^2-4(a)(c) >= 0
Here a = 1 and b = 1; then,
1^2-4(1)(c) >= 0
-4(c) >= -1
c <= -1/-4
c <= 0.25
