Question

is there any method instead of hit and trial method for this question :
the inequality b^2+5>9b+12 is satisfied if :
a) b>9 or b<1
b) b>9 or b<0
c) b=10 or b=-1
d) b>8 or b< 0

Answer 1

help me any1

Answer 2

Even without given answer choices, I've always been taught to do these, at least the quadratic inequalities, with a guess-and-check method.

Have you heard of doing it where you find the roots of the quadratic inequality, plot them on a number line, and then test 3 numbers-- one number less than your first plot, one number that's between your plots, and the last number that's greater than your second plot? You find your answer based on whether the section of your number line you tested it "true" or "false". Am I making sense?

Answer 3

yes , it is being making whole sense :) , thanks so finally hit and trial is best for these type of questions m i right!111

Answer 4

Yep, hit and miss is the way to go.

Answer 5

thanks

Answer 6

rogster is this method correct :
b^(2)+5>9b+12

Since 9b contains the variable to solve for, move it to the left-hand side of the inequality by subtracting 9b from both sides.
b^(2)+5-9b>12

Move all terms not containing b to the right-hand side of the inequality.
b^(2)-9b+5>12

To set the left-hand side of the inequality equal to 0, move all the expressions to the left-hand side.
b^(2)-9b-7>0

Use the quadratic formula to find the solutions. In this case, the values are a=1, b=-9, and c=-7.
b>(-b\~(b^(2)-4ac))/(2a) where ab^(2)+bb+c=0

Substitute in the values of a=1, b=-9, and c=-7.
b>(-(-9)\~((-9)^(2)-4(1)(-7)))/(2(1))

Multiply -1 by the -9 inside the parentheses.
b>(9\~((-9)^(2)-4(1)(-7)))/(2(1))

Simplify the section inside the radical.
b>(9\~(109))/(2(1))

Simplify the denominator of the quadratic formula.
b>(9\~(109))/(2)

First, solve the + portion of \.
b>(9+~(109))/(2)

Next, solve the - portion of \.
b>(9-~(109))/(2)

To find the solution set that makes the expression greater than 0, break the set into real number intervals based on the values found earlier.
b<(9-~(109))/(2)_(9-~(109))/(2)<b<(9+~(109))/(2)_(9+~(109))/(2)<b

Determine if the given interval makes each factor positive or negative. If the number of negative factors is odd, then the entire expression over this interval is negative. If the number of negative factors is even, then the entire expression over this interval is positive.
b<(9-~(109))/(2) makes the expression positive_(9-~(109))/(2)<b<(9+~(109))/(2) makes the expression negative_(9+~(109))/(2)<b makes the expression positive

Since this is a 'greater than 0' inequality, all intervals that make the expression positive are part of the solution.
b<(9-~(109))/(2) or b>(9+~(109))/(2)

Answer 7

Give me a minute, I have to do my own homework :/

Answer 8

ok , sorry :(

Answer 9

I'm not going to able to get to this tonight. So sorry!