the product of two consecutive integers is 420. which quadratic equation can be used to find x, the lesser…

the product of two consecutive integers is 420. which quadratic equation can be used to find x, the lesser number?\n$x^{2}+1 = 420$\n$x^{2}+2 = 420$\n$x^{2}+x = 420$\n$x^{2}+2x = 420$

the product of two consecutive integers is 420. which quadratic equation can be used to find x, the lesser number?\n$x^{2}+1 = 420$\n$x^{2}+2 = 420$\n$x^{2}+x = 420$\n$x^{2}+2x = 420$

Answer

Explanation:

Step1: Define the two consecutive integers

Let the lesser integer be $x$. Then the greater consecutive integer is $x + 1$.

Step2: Set up the product - equation

The product of the two consecutive integers is $x(x + 1)$. We know it is equal to 420. So, $x(x + 1)=420$.

Step3: Expand the left - hand side

Using the distributive property $a(b + c)=ab+ac$, where $a = x$, $b=x$ and $c = 1$, we get $x^{2}+x=420$.

Answer:

C. $x^{2}+x = 420$