Question

a,ß are zeroes of the quadratic polynomial x2 - (k+6)x + 2(2k-1).
Find the values of k if a +B=aß.​

Answer 1

Step-by-step explanation:

a+b=ab

k+6=2(2k-1)

k+6=4k-2

3k=8

k=8/3

Answer 2

Given :

• α and β are the zeroes of the quadratic polynomial x² - (k+6)x + 2(2k-1).
• α + β = αβ

To find :

• The value of k.

Solution:

We know that,

The standard form of a quadratic polynomial is ax² + bx + c. Here,

• a = 1
• b = - (k + 6)
• c = 2(2k - 1)

Also, we know ;

Sum of zeroes = $\sf \dfrac{-(coefficient \: of \: x)}{coefficient \: of \: x^2}$

⇒ α + β = $\sf \dfrac{-\{-(k+6)\}}{1}$

⇒ α + β = k + 6 ️ ️

⇒ αβ = k + 6 ..... (i)

[ ∵ α + β = αβ ]

Product of zeroes = $\sf \dfrac{constant \: term}{coefficient \: of \: x^2}$

⇒ αβ = $\sf \dfrac{2(2k-1)}{1}$

⇒ αβ = 2(2k - 1) ..... (ii)

From (i) and (ii),

⇒ k + 6 = 2(2k - 1)

⇒ k + 6 = 4k - 2

⇒ 4k - k = 6 + 2

⇒ 3k = 8

⇒ k = $\sf \dfrac{8}{3}$

Hence, the value of k is 8/3.