1.

Find the value of k such that the polynomial x2-(k+r)x+2(2k-1)

Answer»

Answer:

Hello:

Step-by-step explanation:

Let α and β are the roots of GIVEN quadratic equation x² - ( k +6)x + 2(2k +1) = 0 [ you did mistake in typing of equation , I just CORRECT it ]

Now, sum of roots = α + β = - {-( k + 6)}/1 = (k + 6)

product of roots = αβ = 2(2k + 1)/1= 2(2k + 1)

A/C to QUESTION,

sum of roots ( ZEROS ) = 1/2 × products of roots zeros

⇒ (k + 6) = 1/2 × 2(2k + 1)

⇒ (k + 6) = (2k + 1)

⇒ k + 6 = 2k + 1

⇒ k = 5

Hence, k = 5


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