4x^2+8x-m=0,differs by 3 find the value of the constant m
plz help me??
differs from what by 3 ?
do you mean the roots differ by 3 or something?
Yes the root
ok
x = [ -8+/- sqrt (64-16m) ]/8
so
(1/8) * 2 * sqrt (64-16 m) = 3
sqrt (64 - 16 m) = 12
64 - 16 m = 144
16 m = 80
m = 5
If
64-16m=144
-16m=80
m=-5? Can it be negative
To find the value of the constant m in the equation 4x^2 + 8x - m = 0, given that it differs by 3, we can use the concept of factoring the quadratic equation.
Step 1: Rewrite the equation in the standard form: ax^2 + bx + c = 0
In this case, we have 4x^2 + 8x - m = 0.
Step 2: Identify the values of a, b, and c in the equation.
Here, a = 4, b = 8, and c = -m.
Step 3: Use the fact that the quadratic equation differs by 3, which means the -b coefficient (8 in this case) should be equal to 3 times the square root of the product of a and -c (4 * -m) to set up an equation.
So, -b = 3√(a(-c))
Substituting the values:
-8 = 3√(4 * (-m))
-8 = 3√(-4m)
Step 4: Solve for m.
Cube both sides of the equation to eliminate the cube root:
(-8)^3 = (3√(-4m))^3
-512 = 27 * -m
-512 = -27m
Divide both sides by -27 to isolate m:
m = -512 / -27
m ≈ 18.963
Therefore, the value of the constant m is approximately 18.963.