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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 +
Question: a. What is the inverse of f (x)? b. Graph the inverse function from part (a). c. Rewrite the inverse function from part (a) in exponential form. d. Evaluate
Here we need to see the inverse of a matrix. Provided a square matrix, A, of size n x n if we can get the other matrix of similar size, B that, AB = BA = I n after that we call
40.783-75
1.If a+b=2b and ab+cd+ad=3bc,prove that a,b,c,d are in A.P 2.The nth term of an A.P is an+b.Find the sum of the series upto n terms.
There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys
A washing machine, cash price $ 850 is available on the following terms: A deposit of $ 100 followed by equal payments at the end of each month for the next 18 months, if intere
Curvature - Three Dimensional Space In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require → r′ (t) is continuou
If 967.234 is divided by 10, how will the decimal point move? It will move one place to the left. While dividing by multiples of 10, the decimal point is moved to the left acco
Two 1000 liter tanks are containing salt water. Tank 1 has 800 liters of water initially having 20 grams of salt dissolved in this and tank 2 has 1000 liters of water and initially
wha is intergration?
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