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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 +
sin45
Describe Independent Events in maths? Events are independent if the outcome of one event does not affect the outcome of the second event. If A represents one independent event
The centre of a circle is (2x - 1, 3x + 1).Find x if the circle passes through (-3,-1) and the length of the diameter is 20 units.
3x^2+19x-14=0
there are 300 students in the sixth grade. if 40% of them were girls, how many boys were there?
In this section we will consider for solving first order differential equations. The most common first order differential equation can be written as: dy/dt = f(y,t) As we wil
how many sixs are in 60
example
calculate x+2+y=4
What is the ratio of the areas of sectors I and II ? (Ans:4:5) Ans: Ratio will be 120/360 Π r 2 : 150/360 Π r 2 4/12 : 5/12 =
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