Choose the correct answer for (x^2+14x+49=0).

Correct answer: two real and equal roots

Here, \(a=1\), \(b=14\), and \(c=49\). Thus, the discriminant is \(D=b^2-4ac=14^2-4(1)(49)=196-196=0\). When \(D=0\), the two roots are real and equal. In fact, the equation can be written as \((x+7)^2=0\), giving the repeated root \(-7\). Exam tip: choose equal real roots for \(D=0\); distinct real roots require \(D>0\).