Question

If x-2 is a factor Of x2-ax+4,then the value of a is

Answer 1

Let P(x) = x² - ax + 4

F(x) = x - 2

F(x) = 0

➱ x - 2 = 0

➱ x = 2

By Remainder Theorem, (x - 2) will be a factor of P(x), if P(x) = 0

Now,

P(2) = 0

Then, x² - ax + 4 = 0

⠀⠀⠀⠀➦ 2² - 2a + 4 = 0

⠀⠀⠀⠀➦ 4 + 4 - 2a = 0

⠀⠀⠀⠀➦ 8 - 2a = 0

⠀⠀⠀⠀➦ 2a = 8

⠀⠀⠀⠀➦ a = 4

Hence the value of a is 4

Additional Information

Remainder Theorem

Remainder theorem is a method in which we find the remainder without attempting long Division method for polynomials

The Remainder Theeom was Discovered by Etienne Bezout

Answer 2

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$\rm\orange{a=4}$

Let P(x) = x² - ax + 4

F(x) = x - 2

F(x) = 0

x - 2 = 0

x = 2

By Remainder Theorem, (x - 2) will be a factor of P(x), if P(x) = 0

P(2) = 0

Then, x² - ax + 4 = 0

⠀⠀⠀⠀ 2² - 2a + 4 = 0

⠀⠀⠀⠀ 4 + 4 - 2a = 0

⠀⠀⠀⠀ 8 - 2a = 0

⠀⠀⠀⠀ 2a = 8

⠀⠀⠀⠀ a = 4

Hence the value of a is 4.

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