If p(x) = 4x2 + 4x + 1= 0, then discriminate (D) = 0. true or false
Answers
Answer:
It is True .
Step-by-step explanation:
How do you find the value of ‘p’, if the following quadratic equation has equal roots: 4x2−(p−2)x+1=0 ?
What are some do’s and don’ts for investing in mutual funds?
Investing in mutual funds can be considered as one of the simple, yet convenient ways chosen by individuals with an aim to create
4x^2 - (p-2)x + 1 = 0
x1 = [(p-2) + (p^2–4p+4–4)^0.5]/8
x2 = [(p-2) - (p^2–4p+4–4)^0.5]/8
Since the roots are equal x1 = x2, or
[(p-2) + (p^2–4p+4–4)^0.5]/8 = [(p-2) - (p^2–4p+4–4)^0.5]/8 or
[(p-2) + (p^2–4p+4–4)^0.5]= [(p-2) - (p^2–4p+4–4)^0.5] or
(p^2–4p+4–4)^0.5 = - (p^2–4p+4–4)^0.5], or
2(p^2–4p+4–4)^0.5 = 0
4(p^2–4p+4–4) = 0^2 = 0
4p(p-4) = 0
p = 0 or 4 Answer.
Check: If p =0. 4x^2 - (p-2)x + 1 = 0 becomes
4x^2 +2x + 1 = 0. Its roots are [-2+(4–4)^0.5]/8 = -1/4
If p =4. 4x^2 - (p-2)x + 1 = 0 becomes
4x^2-2x + 1 = 0. Its roots are [-2-(4–4)^0.5]/8 = -1/4
The two roots are -(1/4) and the same. Correct.