Question

If ∝ and β are the roots of the quadratic polynomial p(x)= 3x²+(k-2)x(3k-2). Find k if ∝+β=2∝β

Answer fast

Answer 1

Heya!!

FOR A GENERAL QUADRATIC EQUATION

ax² + bx + c = 0

Alfa + beta = -b/a

And

Alfa × Beta = c/a

______________________________

p( x ) = 3x² + ( k - 2 )x + 3k -2

Alfa + beta = ( 2- k )/ 3

And

Alfa × beta = ( 3k - 2 ) / 3

ACCORDING TO THE QUESTION

( 2 - k )/3 = 2× ( 3k -2 ) /3

=>

( 2 - k ) = 2 ×( 3k -2 )

=>

k = 6/7