Question

in the following find whether the given quadratic equation have real roots and if so find the roots
$9 {x}^{2} - 9 (a + b)x + ( {2a}^{2} + 5ab + {2b}^{2} )= 0$
​

Answer 1

Answer:

★ QUADRATIC RESOLUTION ★

GIVEN EQUATION :

9x² - 9( a+b)x + (2a² + 5ab + 2b² ) = 0

BY QUADRATIC FORMULA -

9 ( a + b ) ± √ 81(a+b)² - 4 (9)( 2a² + 5ab + 2b² ) / 2( 9 )

RESOLVING " D " SEPARATELY :

81 ( a + b ) ² - 4 ( 9 )( 2a²+5ab+2b² )

81( a² + b² + 2ab ) - 36( 2a²+5ab+2b² )

81a²+81b²+ 162ab - 72a²- 180ab - 72b²

9a² + 9b² -18ab = [3(a+b)]²

D = [3(a+b)]² ; √D = 3( a+b )

9( a+b ) ± 3 ( a + b ) / 18

yields two values or roots respectively ,

2/3 ( a + b ) ; a+b /3

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★.

Answer 2

Answer:

hisbsksfjsabckjgxgvlkyvjcx