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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 +
To find out the perimeter of a triangular region, what formula would you use? The perimeter of a triangle is length of surface a plus length of side b plus length of side c.
Rental car agency has 50 cars. Rental rate in winter is 60%. What is probability that in give winter month the rental rate is fewer than 35 cars rented? Use normal distribution to
1. Show that there do not exist integers x and y for which 110x + 315y = 12. 2. If a and b are odd integers, prove that a 2 +b 2 is divisible by 2 but is NOT divisible by 4. H
ABCD is a parallelogram in the given figure, AB is divided at P and CD and Q so that AP:PB=3:2 and CQ:QD=4:1. If PQ meets AC at R, prove that AR= 3/7 AC. Ans: ΔAPR ∼ Δ
i do not understand the rules for adding and subtracting integers, nor do i understand how to multiply and divide
1000 time 1000000
Convert each of the following points into the specified coordinate system. (a) (-4, 2 Π /3) into Cartesian coordinates. (b) (-1,-1) into polar coordinates. Solution
Without solving, find out the interval of validity for the subsequent initial value problem. (t 2 - 9) y' + 2y = In |20 - 4t|, y(4) = -3 Solution First, in order to u
Determine the solution to the subsequent differential equation. dv/dt = 9.8 - 0.196v Solution Initially we require finding out the differential equation in the accurate
Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35°N and New Orleans has latitude 30°N. Find the distance between these
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