1
vote
1answer
69 views

A Cubic Equation

$2x^3+ax^2+bx+4=0$, $(a,b \in R^+)$ has three real roots. Then : A. $a\geqslant 4.2^{\frac 1 3}$ B. $a\geqslant 1.2^{\frac 1 3}$ C. $a\geqslant 6.2^{\frac 1 3}$ D. $a\geqslant 2.2^{\frac 1 3}$ ...
4
votes
2answers
72 views

Integral values of an expression

Let $b=\sqrt{a^2+5a+8}-\sqrt{a^2-3a+4}$ Find number of integral values of b. My $long$ way using Calculus : Find domain of function : $R$ Note that function is continuous Prove the function is ...
-1
votes
1answer
48 views

Finding the rule of a quadratic graph

I am trying to find the rule. Insofar: $y = a(x-b)^2 + c$ Turning point is $ (1,9) $ So $ b = 1 $ and $ c = 9 $ $y = a(-4-1)^2 + 9$ $-16 = a(-4-1)^2 + 9 $ $-25 = a (-4-1)^2 $ $-25 = a (-5)^2 ...
0
votes
2answers
31 views

Find quadratic equation based on 2 tangents

I would like to know a way to find an quadratic equation that had 2 given tangents: For example here is 2 tangents equations: y = 1/2 x y = 2 x + 2 and 2 abscisses x = 0 x = 3 Is there a ...
3
votes
1answer
365 views

Finding coefficients of quadratic given one tangent and point on the curve

I am given a quadratic equation: $$ y = Ax^2 + Bx + C $$ that passes through $(1,3)$ and $(2,3)$, and a tangent to the curve is $x - y + 1 = 0$ at $(2.3)$. How do I find $A$, $B$, and $C$? The ...
5
votes
3answers
240 views

What are a , b and c?

$$y = ax^2 + bx + c$$ which is tangent at the origin with the line $y=x$, It is also tangential with the line $y=2x + 3$. Determine the function! Draw a figure! My main question is this solvable? I ...
3
votes
2answers
261 views

Integrating $\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x$

I've been trying to integrate this: $$\int_0^\infty \frac{1}{x^2 + 2x + 2} \mathrm{d} x .$$ Unfortunately I haven't found a way so far. I've been trying to factor the denominator in order to end up ...
5
votes
2answers
596 views

Find equation of quadratic when given tangents?

I know the equations of 4 lines which are tangents to a quadratic: $y=2x-10$ $y=x-4$ $y=-x-4$ $y=-2x-10$ If I know that all of these equations are tangents, how do I find the equation of the ...