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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 +
Two people are 50 feet separately. One of them begin walking north at rate so that the angle illustrated in the diagram below is changing at constant rate of 0.01 rad/min. At what
2x=3+x
how do you convert ft to yds, yds to in,and etr
Recall also which value of the derivative at a specific value of t provides the slope of the tangent line to the graph of the function at that time, t. Thus, if for some time t the
Barbara is packing a wedding gift that is contained within a rectangular box 20 by 18 by 4 in. How much wrapping paper will she require? a. 512 in 2 b. 1,440 in 2 c. 1,0
Concrete to Abstract : Mathematics, like all human knowledge, grows out of our concrete experiences. Let us take the example of three-dimensional shapes. Think about how you came
The sum of the squares of two consecutive positive odd integers is 74. What is the value of the smaller integer? Let x = the lesser odd integer and let x + 2 = the greater odd
Larry earned $32,000 per year. Then he received a (3)1/4% rise. What is Larry's salary after the raise? If Larry earns a (3) 1/4 % (or 3.25%) raise, he will earn 103.25% of his
On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.
Complex numbers from the eigenvector and the eigenvalue. Example1 : Solve the following IVP. We first require the eigenvalues and eigenvectors for the given matrix.
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