# Equation

Equation
has one root x1 = 10. Determine the coefficient b and the second root x2.

Result

b =  1.6
x2 =  -8.4

#### Solution:

$$\smash{ b=-(-1 \cdot 10 \cdot 10+84)/10 = \frac{ 8}{5 } = 1.6 \\~\\-x^2 +1.6x +84 =0 \\~\\x^2 -1.6x -84 =0 \\~\\D = 1.6^2 - 4\cdot 1 \cdot (-84) = 338.56 \\~\\D>0 \\~\\ \\~\\x_{1,2} = \frac{ 1.6 \pm \sqrt{ 1.6^2 - 4\cdot 1 \cdot (-84)} }{ 2 \cdot 1 } = \frac{ 1.6 \pm \sqrt{ 338.56 } }{ 2 } \\~\\x_{1,2} = 0.8 \pm 9.2 \\~\\x_{1} = 10 \\~\\x_{2} = -8.4 \\~\\ \\~\\ (x -10) (x +8.4) = 0 }$$

Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

## Next similar examples:

1. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
3. Variations 4/2
Determine the number of items when the count of variations of fourth class without repeating is 552 times larger than the count of variations of second class without repetition.
Quadratic equation ? has roots x1 = -47 and x2 = -79. Calculate the coefficients b and c.
5. Discriminant
Determine the discriminant of the equation: ?
6. Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
7. 2nd class combinations
From how many elements you can create 1081 combinations of the second class?
8. Combinations
From how many elements we can create 990 combinations 2nd class without repeating?