If( x-k ) is a factor of f( x )= 4x³-(3k+2)x²-(k²-1)x+3,then k is
Question
If( x-k ) is a factor of f( x )= 4x³-(3k+2)x²-(k²-1)x+3,then k is
Solution
To find the value of k, we can use the Factor Theorem which states that if (x - k) is a factor of f(x), then f(k) = 0.
So, we substitute x = k in the equation f(x) = 4x³ - (3k + 2)x² - (k² - 1)x + 3.
This gives us:
f(k) = 4k³ - (3k + 2)k² - (k² - 1)k + 3 = 0
Simplify the equation:
4k³ - 3k³ - 2k² - k³ + k + 3 = 0
Combine like terms:
4k³ - 3k³ - k³ - 2k² + k + 3 = 0
This simplifies to:
0 = 0
This equation is always true, regardless of the value of k. Therefore, k can be any real number.
Similar Questions
The value of k for which x – 1 is a factor of the polynomial 4x3+ 3x2 – 4x + k is :-a.3b.0c.1d.- 3
Find the value of k, if x-1 is a factor of polynomial P(x)=4x3+3x2-4x+k.
.If (x-2)is a factor of f(x)=x³+x³-16x+k, then f(x)is divisible by*x+1x-1x-5x+5
If one of the zeroes of the quadratic polynomial (k – 1)x2 + kx + 1 is –3, then the value of k isSelect an answerA4/3B– 4/3C2/3D– 2/3
f one of the two roots of x²- 4x - k = 0 is twice the other roots, then find the value of k.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.