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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 colum proofs
Differentiate following functions. h (t ) = 2t 5 + t 2 - 5 / t 2 We can simplify this rational expression as follows. h (t )
Q. What is Box-and-Whisker Plot? Ans. Line graphs or stem-and-leaf plots become difficult to manage when there is a large amount of data. Box-and-whisker plots help summa
A vertical post stands on a horizontal plane. The angle of elevation of the top is 60 o and that of a point x metre be the height of the post, then prove that x = 2 h/3 .
1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step
A jeweler has bars of 18-carat gold and 12-carat gold. How much of every melted together to obtain a bar of 16-carat gold, weighing 120 gm ? It is given that pure gold is 24 carat.
How to solve this: log x(81) = 4
The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m 3 . Find the rate of change of the volume of grains in the silo from first pri
How many arrangements can be made from the letters of the word " VENUS " such that the order of the vowels remains the same?
It is a fairly short section. It's real purpose is to acknowledge that the exponent properties work for any exponent. We've already used them on integer and rational exponents al
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