Question 18 (2 points) For which value of "c" will the equation below have two distinct real roots? 4x^2-4x+c=0 4 b 1 C -2 d 2

To determine the value of "c" for which the quadratic equation \(4x^2 - 4x + c = 0\) has two distinct real roots, we need to consider the discriminant of the quadratic equation. The discriminant is given by the formula \(D = b^2 - 4ac\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation.<br /><br />For the quadratic equation \(4x^2 - 4x + c = 0\), we have:<br />- \(a = 4\)<br />- \(b = -4\)<br />- \(c = c\) (the value we need to find)<br /><br />The discriminant \(D\) is:<br />\[D = (-4)^2 - 4 \cdot 4 \cdot c\]<br />\[D = 16 - 16c\]<br /><br />For the equation to have two distinct real roots, the discriminant must be greater than zero:<br />\[16 - 16c > 0\]<br /><br />Solving for \(c\):<br />\[16 > 16c\]<br />\[1 > c\]<br /><br />Therefore, the value of \(c\) must be less than 1 for the equation to have two distinct real roots. Among the given options, the correct answer is:<br /><br />b) 1