Question

find the value of k such that difference between zeros of quadratic polynomial x square - 5 x + 3 (k - 1)is 11​

Answer 1

Solution:

We have been given that a quadratic Equation x² - 5x + 3(k-1) such that difference between zeros of quadratic polynomial is 11.

Let α and β are the zeros of Polynomial

∵ We have :

• α - β = 11....(i)

Relationship Between Zeroes:

Sum of Zeroes = -b/a

α + β = -b/a

α+ β = -(-5)/1

• α + β = 5 .....(ii)

On adding Equations (i) and (ii):

α - β= 11

α + α = 5

_________

2α = 16

⇒ α = 16/2

⇒ α = 8

On putting value of α = 8 in equation (i):

α - β= 11

⇒ 8 - β = 11

⇒ β = -3

Now, Product of Zeroes:

⇒ αβ = c/a

⇒ 8 * - 3 = 3k -3

⇒ -24 = 3k - 3

⇒ -24 + 3 = 3k

⇒ k = -21/7

⇒ k = -3

Therefore, Required Value of k is -3.