If two of the four expressions x + y, x + 5y, x – y, and 5x – y are chosen at random, what is the probability that their product will be of the form of x2 – (by)2, where b is an integer?

  1/6

Step-by-step explanation:

The product will only be of the required form if the two chosen factors are of the form (x +by) and (x -by).

For the factor (x+y), there is also a factor (x-y) on the list. For the factor (x+5y), there is no factor (x-5y) available.

So, of the (4·3)/2 = 6 possible ways to choose two expressions from the four given expressions, only one pair of the 6 will have a product of the required form.

The probability is 1/6.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

30.5*10=350$

you have to multiply the number without the decimal point then add it later but if its tenn u must move the place value of the decimal point 1 to the right.