Question

Question :

a and ß are the roots of the quadratic polynomial p(x)=x^2-(k-6)x+2(2k-1).Find the value of k,if a+ß=1/2aß.

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Answer 1

Correct Question:

α and β are the zeroes of the quadratic polynomial p(x) = x² - ( k - 6 )x + 2(  2k - 1 ). Find the value of k, if α + β = ( 1/2 ) × αβ

Answer:

- 5

Step-by-step explanation:

Given :

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

Comparing x² - ( k - 6 )x + 2(  2k - 1 ) with ax² + bx + c we get,

• a = 1
• b = - ( k - 6 )

• c = 2( 2k - 1 )

Sum of zeroes = α + β = - b/a = - { - ( k - 6 ) } / 1 = k - 6

Product of zeroes = αβ = c/a = { 2( 2k - 1 ) } / 1 = 2( 2k - 1 )

Given :

⇒ α + β = ( 1/2 ) × αβ

⇒ k - 6 = ( 1/2 ) × { 2( 2k - 1 ) }

⇒ k - 6 = 2k - 1

⇒ - 6 + 1 = 2k - k

⇒ - 5 = k

⇒ k = - 5

Therefore the value of k is - 5.

Answer 2

Answer:

-5

Step-by-step explanation:

Given

p(x)=x^2-(k-6)x+2(2k-1)

a+ß=1/2aß equation 1

we know that

a+ß = -b/a

and

aß = c/a

in equation

a = 1

b = -(k - 6)

c = 2(2k -1)

a+ß= k - 6

aß = 2(2k -1)

on putting the value in equation 1 we get

a+ß=1/2aß

k - 6 = 2(2k -1)/2

k - 6 = 2k -1

k = -5