Question

If x - 2 is factor of 5x^2-3kx-5,then the value of k is​

Answer 1

Answer:

k = 0.4

Step-by-step explanation:

Let us consider the factor of a quadratic polynomial as g(x)

and the quadratic equation as f(x)

★ According to the question,

• g(x) = (x - 2)
• f(x) = 5x² - 3kx - 5

Since it is mentioned in the question that g(x) is a factor of f(x), by factor theorem;

g(x) = 0

→ x - 2 = 0

→ x = 2

Also,

f(x) = 0

⇒ 5x² - 3kx - 5 = 0

⇒ 5(2)² - 3k(2) - 5 = 0

⇒ 5(4) - 6k - 5 = 0

⇒ 15 - 6k = 0

⇒ 6k = 15

⇒ k = 15 ÷ 6

⇒ k = 0.4

∴ The value of k = 0.4

Answer 2

K = 5/2

Step by Step Explanation :-

TOPIC :-

• Zeros of polynomial

Given :-

p(x) = 5x² - 3kx - 5 = 0

x - 2 is a factor . { indirect clue }

↓

is one of the zero of given polynomial

so , x = 2

To find :-

• value of k

Solution :-

substitute x = 2 in p(x) ,

5(2)² - 3k(2) - 5 = 0

20 - 5 = 6k

k = 15/6 = 5/2

• value of k is 2