Question

If p(x) = 4x2 + 4x + 1= 0, then discriminate (D) = 0. true or false​

Answer 1

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 ?

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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.

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