Q. 35.0( 1 Vote )

# Find the value of k if (x – 5) is a factor of the polynomial x3 – 3x2 + kx – 10.

Using Remainder Theorem:

Putting factor = 0, we get -

(x – 5) = 0

x = 5.

Now, it is given that (x – 5) is a factor of the polynomial x3

3x2 + kx – 10.

If we substitute x = 5 in x3 – 3x2 + kx – 10, the remainder will be zero.

53 – 3(5)2 + k(5) – 10 = 0

125 – 3× 25 + 5k – 10 = 0

125 – 75 + 5k – 10 = 0

5k + 40 = 0 k = – 8

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