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In polynomials you have seen expressions of the form x2 + 3x - 4. Also we know that when an expression is equated to zero or some other expression, we call it an equation. The equations of the second degree in a single variable "x" or "y" are generally referred to as quadratic equations and the most general form of it is
ax2 + bx + c = 0. The roots or solution for the quadratic equation can be obtained by substituting different values for x and selecting that value for which the value of the equation is zero. The methods which we have seen in factorization of polynomials are also applicable to obtain the roots of a quadratic equation. However, in this part we look at a specific method which is only applicable to solve quadratic equations.
According to this method the roots of a quadratic equation ax2 + bx + c = 0 are
x
This is derived as follows. We have
ax2 + bx + c = 0
ax2 + bx = - c ........(1)
In order to make the LHS a perfect square, we add to to the LHS and since the equality is to be preserved we do so for the other side also. Hence we obtain
x2 +
If the point (a,2a) is an interior point of the region bounded by the parabola y2=16x and the double ordinate through the focus then a belongs to
The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?
The time t required to test a computer memory unit is directly proportional to the square of the number n of memory cells in the unit. For a particular type of unit, n = 6400
if oranges cost $2.40 a dozen, how much do 2 oranges cost?
We will look at three types of progressions called Arithmetic, Geometric and Harmonic Progression. Before we start looking at the intricacies of these let us unders
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The 5% sales tax on a basket was $0.70. What was the price of the basket? Use a proportion to solve the problem; part/whole = %/100. The whole is the price of the basket (wh
Primary, note that quadratic is another term for second degree polynomial. Thus we know that the largest exponent into a quadratic polynomial will be a2. In these problems we will
Before searching at series solutions to a differential equation we will initially require to do a cursory review of power series. So, a power series is a series in the form, .
Question: Solve the initial value problem 2x'' +x'-x =27 Cos2t +6 Sin 2t, x(0)=2 , x'(0)= -2 by using Laplace transform method.
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