i need a lil help with this
If x=2 is a root of the equation
6x^3 - px^2 - 14x + 24=0, find p,hence, solve the equation
6*(2)3-p*(2)2-14*2+24=0
6*8-p*4-14*2+24=0
48-4p-28+24=0
Can take it from here?
yes..i got p to be 11.
I do not know what else to do from here to solve the equation
To solve the equation, you have already found the value of p, which is 11.
Now, substitute this value back into the original equation and solve for x.
6x^3 - px^2 - 14x + 24 = 0
Replace p with 11:
6x^3 - 11x^2 - 14x + 24 = 0
To solve this, you can try factoring or using the Rational Root Theorem. If you don't see any factors right away, you can try synthetic division or use a graphing calculator to find the roots.
Let's use synthetic division to find the other roots:
Since x = 2 is already a root, perform the division using synthetic division with (x - 2) as the divisor:
2 | 6 -11 -14 24
12 2 -24
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6 1 -12 0
The result of the division is 6x^2 + x - 12 = 0. Now, we can solve this quadratic equation.
Factor or use the Quadratic Formula to solve 6x^2 + x - 12 = 0:
(2x + 3)(3x - 4) = 0
Setting each factor equal to zero:
2x + 3 = 0 or 3x - 4 = 0
Solving each equation:
2x = -3 or 3x = 4
x = -3/2 or x = 4/3
So, the complete solution to the equation 6x^3 - px^2 - 14x + 24 = 0 is:
x = 2, x = -3/2, x = 4/3