Question

2po
4. If (x - 2) is a factor of
5x2 - kx - 18. then find the
value of k*
​

Answer 1

Answer-

If (x - a) is a factor of p(x) = 5x² - kx - 18, then p( a) = 0

OR

p(a) = 0, where a is zero of the equation (x - a)

[ p(x) = 5x² - kx - 18]

________________________________

• find the zero of (x-2)

⟹ (x - 2) = 0

⟹ x = 0 + 2

⟹ x = 2

________________________________

p(2) = 5(2)² - k(2) - 18 = 0

= 5(4) - 2k - 18 = 0

= 20 - 18 - 2k = 0

= 2 - 2k = 0

= -2k = -2

= k = -2/-2

= k = 1

value of k is 1.

Answer 2

SOLUTION

GIVEN

x - 2 is a factor of 5x² - kx - 18

TO DETERMINE

The value of k

EVALUATION

Let f(x) = 5x² - kx - 18

g(x) = x - 2

For Zero of the polynomial g(x) we have

g(x) = 0

⇒ x - 2 = 0

⇒ x = 2

Since x - 2 is a factor of 5x² - kx - 18

So by the Remainder Theorem

f(2) = 0

⇒ 5 × (2)² - k × 2 - 18 = 0

⇒ 20 - 2k - 18 = 0

⇒ 2 - 2k = 0

⇒ 2k = 2

⇒ k = 1

FINAL ANSWER

Hence the required value of k = 1

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