Question
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
Solution
4.5
(324 Votos)
Quitéria
Elite · Tutor por 8 anos
Resposta
To determine the value of "c" for which the quadratic equation
has two distinct real roots, we need to consider the discriminant of the quadratic equation. The discriminant is given by the formula
, where
,
, and
are the coefficients of the quadratic equation.For the quadratic equation
, we have:-
-
-
(the value we need to find)The discriminant
is:
For the equation to have two distinct real roots, the discriminant must be greater than zero:
Solving for
:
Therefore, the value of
must be less than 1 for the equation to have two distinct real roots. Among the given options, the correct answer is:b) 1