Question

find the value of k such that x+1 is a factor of 5x^3+4x^2-6x+2k​

Answer 1

g(x) = x+1

g(x) = 0 → x+1 = 0

→ x = -1

p(x) = 5x³ + 4x² - 6x + 2k

p(-1) = 5(-1)³ + 4(-1)² - 6(-1) + 2k = 0

→ -5 + 4 + 6 + 2k = 0

→ 2k = -5

→ k = -5/2, or -2.5

Answer 2

Question:-

Find the value of k such that x+1 is a factor of :-

${5x}^{3} + {4x}^{2} - 6x + 2k$

Answer :-

$x + 1 = 0 \\ x = - 1$

Now, Put the value of x

${5x}^{3} + {4x}^{2} - 6x + 2k$

${5 \times ( - 1)}^{3} + {4 \times ( - 1)}^{2} - 6 \times ( - 1) + 2k = 0$

$5 \times ( - 1) + 4 \times 1 - 6 \times ( - 1) + 2k = 0$

$- 5 + 4 + 6 + 2k = 0 \\ 5 + 2k = 0 \\ 2k = - 5 \\ k = \frac{ - 5}{2}$

Hence, the value of k is

-5/2

Hope this helps you...