The quadratic equation that can be used to find x the smaller number is x^2 + x - 272 = 0.
A quadratic equation is a polynomial which has the highest degree equal to two. It is a second-degree equation of the form ax² + bx + c = 0, where a, b, are the coefficients, c is the constant term, and x is the variable.
For the given situation,
Let the integer be x and the consecutive next integer be x+1.
The product of two consecutive integers is 272,
⇒ [tex]x(x+1)=272[/tex]
⇒ [tex]x^{2} +x=272[/tex]
⇒ [tex]x^{2} +x-272=0[/tex]
Hence we can conclude that the quadratic equation that can be used to find x the smaller number is x^2 + x - 272 = 0.
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