If the equations 2 x^3+k x-4=0 and 6 x^4+3 k x^2+2=0 have a common root, k equals (a) (433)/(18)

step 1 So in the given question we are told that if the equations 2x cube 2x cube plus kx minus 4 equal

If the equations 2 x^3+k x-4=0 and 6 x^4+3 k x^2+2=0 have a...

Key Concepts

Polynomial Equations

Polynomial equations involve expressions consisting of variables raised to non-negative integer powers and their coefficients. The understanding of these equations, including their degrees and coefficients, is fundamental in analyzing and solving them, particularly when determining the existence and nature of their roots.

Common Roots

A common root is a value that simultaneously satisfies two or more polynomial equations. The problem of finding a common root typically requires setting up conditions such that when a value is substituted into both polynomials it makes each equation equal to zero, which can lead to determining additional unknown parameters in the equations.

Substitution and Elimination

The substitution method is a technique used to reduce the complexity of equations by expressing one variable or parameter in terms of another. In problems involving common roots, this approach allows one to substitute the expression derived for a parameter from one equation into another, eliminating variables and creating a solvable equation for the unknowns.

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