Question

Find the roots of the equation, if they exists, by applying the quadratic formula :-

$x {}^{2} - (2b - 1)x + (b {}^{2} - b - 20) = 0$

[ CBSE 2015 ]

Answer 1

hey mate
here's the solution

Answer 2

x² - ( 2b - 1) x + ( b² - b - 20 ) = 0.

Discriminat, D = b² - 4ac

D => ( 2b - 1 ) ² - 4 ( b² - b - 20 ) (1 )

D => 4b² + 1 - 4b - 4b ² + 4b + 80

D => 81.

ROOTS EXIST.


BY QUADRATIC FORMULA,

x = [ - b +- √( D ) ] / 2a

x = [ ( 2b - 1 ) +- √ 81 ] / 2

x = [ ( 2b - 1 ) +- 9 ] / 2

x = ( 2b - 1 +9 ) / 2

x = ( 2 b + 8 ) / 2

=> x = b + 4

x = ( 2b - 1 - 9 ) / 2

x = ( 2b - 10 ) / 2

=> x = b - 5