Answer:
[tex]k = -\frac{7}{3}[/tex]
Step-by-step explanation:
Given :
p(x) = 2x² − 3kx + 5
Since, -1 is a zero for p then :
p(-1) = 0
Solving the equation p(-1) = 0 for k :
p(-1) = 0
⇔ 2(-1)² − 3k(-1) + 5 = 0
⇔ 2 + 3k + 5 = 0
⇔ 3k = -5 - 2
⇔ 3k = -7
⇔ k = -7/3
NOTE :
If -1 is a zero of p
[tex]\Longrightarrow k = -\frac{7}{3}[/tex]
[tex]\Longrightarrow p(x) = 2x^2 - 3(\frac{-7}{3}) x + 5\\\Longrightarrow p(x) = 2x^2+ 7x + 5[/tex]
