Question

Find the value of k if the quadratic polynomial x²+2x+k is a factor of the biquadratic polynomial 2x x14x² + 5x +6.

pls answer fast do not tell ant nonsense answer other wise I will report​

Answer 1

Answer:

We get the remainder as open parentheses 21 plus 7 k close parentheses x plus 2 k squared plus 8 k plus 6.

Since, x squared plus 2 x plus k is a factor of the given polynomial, the remainder should be zero.

Hence,

21+7k=0 and 2k2+8k+6=0 at the same time.

k= -3 satisfies both equations. Hence, k=-3.

So we can write the polynomial as

2 x to the power of 4 plus x cubed minus 14 x squared plus 5 x plus 6 equals open parentheses x squared plus 2 x minus 3 close parentheses open parentheses 2 x squared minus 3 x minus 2 close parentheses  

Hence, the zeroes of x squared plus 2 x minus 3 are

x squared plus 2 x minus 3 equals 0 rightwards double arrow x squared plus 3 x minus x minus 3 equals 0 rightwards double arrow x open parentheses x plus 3 close parentheses minus 1 open parentheses x plus 3 close parentheses equals 0 rightwards double arrow open parentheses x plus 3 close parentheses open parentheses x minus 1 close parentheses equals 0 rightwards double arrow x equals negative 3 space o r space x equals 1

The above two are factors of the 4th degree polynomial as well.

The other two roots of the 4th degree polynomial are roots of the quadratic

Step-by-step explanation: