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Example Solve 3x2 - 2 x -11 = 0.
Solution
In this case the polynomial doesn't factor thus we can't do that step. Though, still we do have to know where the polynomial is zero. We ought to use the quadratic formula for that. Here is what the quadratic formula gives us.
x = (1 ± √ 34)/3
In order to work the problem we'll have to reduce this to decimals.
x = (1 +√34)/3 = 2.27698 x = (1 -√34) /3 = -1.61032
From this instance on the procedure is identical to the earlier examples. In the number line below the dashed lines are at the estimated values of the two decimals above & the inequalities illustrate the value of the quadratic evaluated at the test points illustrated.
Thus, it looks like we required the two outer regions for the solution. Here is the inequality & interval notation for the solution.
-∞ < x < (1 - √34 )/3 and ( 1 + √34 )/3 -∞, (1- √ 34) /3 and ( 1 +√34 /3, , ∞ )
-∞, (1- √ 34) /3 and ( 1 +√34 /3, , ∞ )
Finding Zeroes of a polynomial The below given fact will also be useful on occasion in determining the zeroes of a polynomial. Fact If P (x) is a polynomial & we know t
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how do you change this (x+2y=10) equation into "y" form ?
i dont get them i need help
please explain all examples
what is 3.16 x 10^3= ?
These are the only possibilities for solving quadratic equations in standard form. However Note that if we begin with rational expression in the equation we might get different so
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solve the system of equations by graphically and compare the solution with that obtained by matrix approach 3x+2y=8 y=x-1
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