Differentiate the given cubic equation and equate to zero. Solve the roots of the resulting quadratic equation. To have two extremes, the roots of the quadratic equation must be real. What makes the roots real is when the discriminant of the quadratic equation greater than zero.
If you have further question, don't hesitate to ask.
Differentiate the given cubic
Member for
17 years 6 monthsDifferentiate the given cubic equation and equate to zero. Solve the roots of the resulting quadratic equation. To have two extremes, the roots of the quadratic equation must be real. What makes the roots real is when the discriminant of the quadratic equation greater than zero.
If you have further question, don't hesitate to ask.
D ko po makuha yung roots sir
Member for
6 yearsIn reply to Differentiate the given cubic by Jhun Vert
D ko po makuha yung roots sir
$y = ax^3 + bx^2 + cx + d$
Member for
17 years 6 months$y = ax^3 + bx^2 + cx + d$
$y' = 3ax^2 + 2bx + c = 0$
The roots of the quadratic equation are
$x = \dfrac{-B \pm \sqrt{B^2 - 4AC}}{2A}$
$x = \dfrac{-2b \pm \sqrt{4b^2 - 12ac}}{6a}$
To have two extremes
$4b^2 - 12ac \gt 0$
Yan na po value ni x?
Member for
6 yearsIn reply to $y = ax^3 + bx^2 + cx + d$ by Jhun Vert
Yan na po value ni x?
Paano po makuha c 4b²-12ac?
Member for
6 yearsIn reply to $y = ax^3 + bx^2 + cx + d$ by Jhun Vert
Paano po makuha c 4b²-12ac?
Substitute:
Member for
17 years 6 monthsIn reply to Paano po makuha c 4b²-12ac? by Francis June E…
Substitute:
A = 3a
B = 2b
C = c
When i substitute x to y",
Member for
6 yearsWhen i substitute x to y", answer nya po is 2√b²-3ac and -2√b²-3ac?
Pero yung answer daw po is only b²-3ac.
How po?
You don't need to do that.
Member for
17 years 6 monthsIn reply to When i substitute x to y", by Francis June E…
You don't need to do that. Divide 4b2 - 12ac > 0 both sides by 4 and you will get the answer.
Pero paano po nakuha yung
Member for
6 yearsIn reply to You don't need to do that. by Jhun Vert
Pero paano po nakuha yung 4b²-12ac?
When i substitute A,B and C
Member for
6 yearsIn reply to Pero paano po nakuha yung by Francis June E…
When i substitute A,B and C
The answer is -2b+-√4b²-12ac/6a
Paano po naging 4b²-12ac nalang po?
D ko parin pa makuha kung
Member for
6 yearsIn reply to You don't need to do that. by Jhun Vert
D ko parin po makuha kung paano naging b²-3ac nalang
The problem ask for the
Member for
17 years 6 monthsIn reply to D ko parin pa makuha kung by Francis June E…
The problem ask a condition for the cubic to have two extremes. You give "4b2 - 12ac > 0" as your condition to satisfy the problem.
From $x = \dfrac{-2b \pm \sqrt{4b^2 - 12ac}}{6a}$
That is why you give $4b^2 - 12ac \gt 0$ as you answer to satisfy the condition of the problem.
Paano ko po malalaman na 4b²
Member for
6 yearsIn reply to The problem ask for the by Jhun Vert
Okay na po. Salamat po .