Question

If a and b are the zeros of the polynomial x2-5x+k such that a-b=1 find the value of k

Answer 1

Answer:

$\large{\underline{\boxed{\sf k = 6}}}$

Step-by-step explanation:

Given polynomial;

x² - 5x + k, on comparing the given equation with ax² + bx + c, we get-

• a = 1
• b = - 5
• c = k

Sum of zeroes = -b/a

⇒ a + b = - (-5)/1

⇒ a + b = 5 .... (i)

Product of zeroes = c/a

⇒ ab = k/1

⇒ ab = k ... (ii)

It is also given that ;

a - b = 1... (iv)

On adding equation (i) and (iv) -

⇒ a + b + a - b = 5 + 1

⇒ 2a = 6

⇒ a = $\sf \dfrac{6}{2}$

⇒ a = 3

Putting the value of a in (i),

⇒ a + b = 5

⇒ 3 + b = 5

⇒ b = 5 - 3

⇒ b = 2

Substituting the value of a and b in (ii),

⇒ ab = k

⇒ 3 * 2 = k

⇒ 6 = k

⇒ k = 6

Hence, the value of k is 6.