(what is the meaning of this question)
If the root of the equation x²-8x+m=0 exceeds the other by 4 then the value of m is
the roots are
x = (8±√(64-4m))/2 = 4±√(16-m)
So, we have
4+√(16-m) = 4-√(16-m) + 4
2√(16-m) = 4
√(16-m) = 2
16-m = 4
m = 12
So, the function is
x^2-8x+12, and the roots are 2 and 6
The meaning of the question is asking for the value of "m" in the equation x²-8x+m=0, where the root of the equation exceeds the other root by 4.
The meaning of this question is to find the value of the constant 'm' in the given quadratic equation, where one of the roots is 4 greater than the other.
To solve this, you need to use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the roots are given by:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, the equation is x² - 8x + m = 0. Comparing it with the standard form, we have a = 1, b = -8, and c = m.
Since we know that one root exceeds the other by 4, let's assume the smaller root is k. Then the larger root would be k + 4.
Using the quadratic formula, we can calculate the roots of the equation:
First root, k:
k = (-(-8) - √((-8)² - 4(1)(m))) / (2(1))
k = (8 - √(64 - 4m)) / 2
Second root, k + 4:
k + 4 = (-(-8) + √((-8)² - 4(1)(m))) / (2(1))
k + 4 = (8 + √(64 - 4m)) / 2
Since one root exceeds the other by 4, we can equate these two expressions:
(8 - √(64 - 4m)) / 2 = (8 + √(64 - 4m)) / 2
To simplify, we can cross-multiply and solve for m:
8 - √(64 - 4m) = 8 + √(64 - 4m)
Now, add √(64 - 4m) to both sides:
8 = 8 + 2√(64 - 4m)
Simplify:
0 = 2√(64 - 4m)
To solve for m, we need to isolate the radical term. Divide both sides of the equation by 2:
0 = √(64 - 4m)
Now, square both sides:
0 = 64 - 4m
Rearrange the equation:
4m = 64
Finally, solve for m by dividing both sides by 4:
m = 64/4
m = 16
Therefore, the value of m is 16.