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1 point
14. consider the polynomial
p(x) = 2x“ – (m + 3)x – 1.
If p(x) is divisible by x-2 then m=

Sagot :

xero099

Answer:

If [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]m = \frac{1}{2}[/tex].

Step-by-step explanation:

Let [tex]p(x) = 2\cdot x^{2}-(m+3)\cdot x - 1[/tex], if [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]p(2) = 0[/tex]. That is:

[tex]2\cdot 2^{2}-(m+3)\cdot (2)-1 = 0[/tex]

[tex]8 - 2\cdot m -6 -1 = 0[/tex]

[tex]1 -2\cdot m = 0[/tex]

[tex]2\cdot m = 1[/tex]

[tex]m = \frac{1}{2}[/tex]

If [tex]p(x)[/tex] is divisible by [tex]x-2[/tex], then [tex]m = \frac{1}{2}[/tex].

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