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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 +
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A surveyor is hired to calculate the width of a river. Using the example provided, Calculate the width of the river. a. 48 ft b. 8 ft c. 35 ft d. 75 ft
Kristen earns $550 each week after taxes. She deposits 10% of her income in a savings account and 7% in a retirement fund. How much does Kristen have left after the money is taken
Generate a 1000 vertex graph adding edges randomly one at a time. How many edges are added before all isolated vertices disappear? Try the experiment enough times to determine ho
98+3
Universal set The term refers to the set which contains all the elements such an analyst wishes to study. The notation U or ξ is usually used to denote universal sets.
Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbles as Sam?
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Raul has 56 bouncy balls. He puts three times as many balls into red gift bags as he puts into green gift bags. If he puts the same number of balls in each bag, how many balls does
x ?8x ?16x ? 0, x?0? ? 0, x?0? ? 2
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