For which parameter p has the quadratic equation x^2 − px + 4 = 0 no solution in domain ℝ?
a) p = ±4
b) p∈(−4, 4)
c) p∈(−∞,−4)U(−4,∞)
d) p∈ℝ
e) ℝ\{±4}
The answer is B, but my questions are:
1. What is the question asking(I don't understand)
2. Solve the problem step by step, with worded explanations. Thank you
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Firstly i want to say i am a Chinese so my English isn't very well,but i am quite good at Mathematics.
I don't know whether u have learned something about the root discriminant about quadratic equation.It is
∆, we order ∆=b^2-4ac(when the equation is ax^2+bx+c=0,"a "can't be zero. ).when ∆>0,the equation has two solutions and they are not equal at the same time.If ∆=0 ,the equation has only a solution,If ∆<0,the equation no solution.
In this problem that u have shown,a=1,b=-p c=4.If it has no solution,you just let the ∆<0.it means (-p)^2-4*1*4<0 and you solve this equation ,you will get the answer is B.
By the way,please memory the solution i have told you,because it can help you solve all problems like this.