Home
Class 12
MATHS
Determine the value of k for which x+2 i...

Determine the value of `k` for which `x+2` is a factor of `(x+1)^7+(2x+k)^3dot`

Text Solution

Verified by Experts

The correct Answer is:
`k = 5`
Let `f(x) = (x + 1)^(7) + (2x + k)^(3)` . Now
`f(-2) = (-2+ 1)^(7)+ (-4 + k)^(3) = 0`
or `(k-4)^(3) - 1 =0`
or ` k = 5`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.3|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.4|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|3 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

Determine the value of k for which x-1 is a factor of (x^2 +1)+(x+k)dot

Determine the value of k for which g(x) is a factor of f(x) of the following given polynomials : f(x)=x^(3)+2kx^(2)-11x+k-5andg(x)=2x+1 .

Determine the value of k for which g(x) is a factor of f(x) of the following given polynomials : f(x)=2x^(4)+3x^(3)-kx^(2)+x-6andg(x)=2x+3 .

Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^2+(2p-9)x+6. Find the remaining factor for this value of pdot

Determine the value of k for which the polynomial (2x^(4)-3x^(3)-x^(2)+x+k) is divisible by (2x - 1).

Determine the value of k for which the polynomial (2x^(4)-3x^(3)-x^(2)+x+k) is divisible by (2x + 3).

Determine the values of a and b if x^(2)-4 is a factor of the polynomial ax^(4)+2x^(3)-3x^(2)+bx-4

Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

Consider the ellipse (x^2)/(f(k^2+2k+5))+(y^2)/(f(k+11))=1. If f(x) is a positive decreasing function, then the set of values of k for which the major axis is the x-axis is (-3,2)dot the set of values of k for which the major axis is the y-axis is (-oo,2)dot the set of values of k for which the major axis is the y-axis is (-oo,-3)uu(2,oo) the set of values of k for which the major axis is the y-axis is (-3,-oo,)

Find the value of k for which the given value is a solution of the given equation x^2+3ax+k=0 at x=-a