Question

4x²-2(a²+b²)x+a²b²=0 factorise the quadratic polynomial​

Answer 1

AnswEr :

Given Equation,

$\sf \: 4 {x}^{2} - 2( {a}^{2} + {b}^{2} )x + {a}^{2} {b}^{2} = 0$

Expanding the equation,

$\longrightarrow \: \sf \: {4x}^{2} - 2 {a}^{2}x - {2b}^{2}x + {a}^{2} {b}^{2} = 0$

Now,

$\longrightarrow \: \sf \: 2x(2x - {a}^{2} ) - {b}^{2} (2x - {a}^{2} ) = 0 \\ \\ \longrightarrow \: \sf \: (2x - {a}^{2} )(2x - {b}^{2} ) = 0 \\ \\ \longrightarrow \: \sf \: 2x - {a}^{2} =0 \: or \: \: 2x - {b}^{2} = 0 \\ \\ \longrightarrow \: \sf \: x = \dfrac{ {a}^{2} }{2} \: or \: \: \dfrac{ {b}^{2} }{2}$

The roots of the above equation are a²/2 and b²/2

Answer 2

$\tt{\huge{\orange {Hello!!! }}} C.D$

QUESTION :

4x²-2(a²+b²)x+a²b²=0 factorise the quadratic polynomial

SOLUTION :

Factorising :

4 x^2 - 2 ( a^2 + b^2 ) x + a^2b^2

=> 4 x^2 - 2 a^2 x - 2 b^2 x + a^2 b^2

=> 2X ( 2 X - a^2 ) - b^2 ( 2 x - a^2 )

=> ( 2 X - a ^ 2 ) ( 2 x - b^2 )

The Zeroes of the Polynomial are :

=> 2 X = a^2

=> X = a^2 / 2.........[ Root 1 ]

=> 2 X = b^2

=> X = b^2 / 2 .......... [ Root 2 ]

Answer :

The result from Factorising :

=> ( 2 X - a ^ 2 ) ( 2 x - b^2 )

Roots :

=> X = a^2 / 2.........[ Root 1 ]

=> X = b^2 / 2 .......... [ Root 2 ]