Question

factorise 24x^2-(a+41)+(b+11)a=0,b=1/a=1,b=0. factorise in both situation

Answer 1

if a=0 ,b= 1
24x^2 - (0+ 41)+(1+11)
24x^2 - 41+ 12
24x^2 -29

if a=1,b=0
24x^2 -(1+41)+(0+11)
24x^2 -42+ 11
24x^2 -31

Answer 2

24x² - (a + 41)x + (b+11)

when, b = 1/a = 1
24x² - (1 + 41)x + (1 + 11)1 =0
24x² - 42x + 12 =0
4x² - 7x + 2 =0
x² - 7/4x + 1/2 =0
x² - 2.(7/8)x + (7/8)² = -1/2 + (7/8)²
(x -7/8)² = {√17/8}²
(x - 7/8)² - {√17/8}² = 0
{x - 7/8 + √17/8}{x - 7/8 -√17/8} = 0


when, a = 0, b = 0
24x² -(0 + 41)x + (0+11) = 0
24x² - 41x + 11 = 0
24x² - 8x - 33x + 11 = 0
8x (3x - 1) -11( 3x -1) = 0
(8x -1)(3x -1) = 0