If S represents the greater of the two solutions of the equation
x^2 - 4x - 3 = 5, then :
A) S>3
B) S<3
C) S=3
D) relationship cannot be determined
and why ?
I don't understand this one at all.
x^2 - 4x - 3 = 5
x^2 - 4x - 8 = 0
using the formula I got x = 2 +/- √12
the larger of which is clearly > 3
how did you figure out the formula ?
I was talking about the quadratic formula
for ax^2 + bx + c = 0
x = (-b ± √(b^2 - 4ac))/(2a)
remember that?
Oh, I see now.
sorry.
To determine the value of S, we can start by rewriting the given equation:
x^2 - 4x - 3 = 5
To isolate x, we can move the constant term to the right side of the equation:
x^2 - 4x - 3 - 5 = 0
x^2 - 4x - 8 = 0
By applying the quadratic formula, we can find the solutions for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 1, b = -4, and c = -8. Substituting the values, we have:
x = (4 ± √((-4)^2 - 4(1)(-8))) / (2(1))
x = (4 ± √(16 + 32)) / 2
x = (4 ± √48) / 2
x = (4 ± 4√3) / 2
x = 2 ± 2√3
Since S represents the greater of the two solutions, we can conclude that S = 2 + 2√3.
Now, we can compare S to 3:
S = 2 + 2√3 ≈ 5.464
Comparing S to 3, we can say that S is greater than 3. Therefore, the correct answer is A) S > 3.