5)4x² - 3x + k
4x(-2)²-3x2+k=0
4x4-6+k=0
16-6+k=0
10+k=0
k=-10
Step-by-step explanation:
Find k if -2 is a zero of polynomial 4x²-3x+k
Given here,
p(-2)= 0
[tex] \longrightarrow \sf \: p(x) = 4 {x}^{2} - 3x + k [/tex]
[tex] \longrightarrow \sf \: p( - 2) = 4( - 2 {)}^{2} - 3( - 2) + k = 0\\ [/tex]
[tex] \longrightarrow \sf \: 4 \times 4 \: - \: 3 \times 4 + k = 0[/tex]
[tex] \longrightarrow \sf \: 16 - 12 + k = 0[/tex]
[tex] \longrightarrow \sf \: 4 + k = 0[/tex]
[tex] { \dashrightarrow{\fbox {\bf{k = - 4}}}}[/tex]
➡️ The value of k is -4
Determine whether (x-2) is a factor of 7x²-2√8x-6
Let us assume that
x-2 is a factor of p(x)
x= 2 is a zero of p(x)
[tex] \longrightarrow \sf \: p(2) = 7 {(2)}^{2} - 2 \sqrt{8(2)} - 6 \\ [/tex]
[tex] \longrightarrow \sf \: 14 - 2 \sqrt{16} - 6[/tex]
[tex] \longrightarrow \sf \: 14 - 2 \times 4 - 6[/tex]
[tex] \longrightarrow \sf \: 14 - 8 - 6[/tex]
[tex] \longrightarrow \sf \: 14 - 14 = 0[/tex]
(x-2) is a factor of p(x).
Hence verified ☯️
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Answers & Comments
5)4x² - 3x + k
4x(-2)²-3x2+k=0
4x4-6+k=0
16-6+k=0
10+k=0
k=-10
Step-by-step explanation:
Hope it's help you .if helpful then mark me as brainliest.okay good afternoon
Question 1:
Find k if -2 is a zero of polynomial 4x²-3x+k
Solution:
Given here,
p(-2)= 0
[tex] \longrightarrow \sf \: p(x) = 4 {x}^{2} - 3x + k [/tex]
[tex] \longrightarrow \sf \: p( - 2) = 4( - 2 {)}^{2} - 3( - 2) + k = 0\\ [/tex]
[tex] \longrightarrow \sf \: 4 \times 4 \: - \: 3 \times 4 + k = 0[/tex]
[tex] \longrightarrow \sf \: 16 - 12 + k = 0[/tex]
[tex] \longrightarrow \sf \: 4 + k = 0[/tex]
[tex] { \dashrightarrow{\fbox {\bf{k = - 4}}}}[/tex]
➡️ The value of k is -4
Question 2:
Determine whether (x-2) is a factor of 7x²-2√8x-6
Solution:
Let us assume that
x-2 is a factor of p(x)
x= 2 is a zero of p(x)
[tex] \longrightarrow \sf \: p(2) = 7 {(2)}^{2} - 2 \sqrt{8(2)} - 6 \\ [/tex]
[tex] \longrightarrow \sf \: 14 - 2 \sqrt{16} - 6[/tex]
[tex] \longrightarrow \sf \: 14 - 2 \times 4 - 6[/tex]
[tex] \longrightarrow \sf \: 14 - 8 - 6[/tex]
[tex] \longrightarrow \sf \: 14 - 14 = 0[/tex]
(x-2) is a factor of p(x).
Hence verified ☯️