Question

factorise Ч√3x^2 + 5x -23​

Answer 1

Answer :  

Given : 1/(x - 3)  +  2/(x - 2)  = 8/x

[1(x - 2) + 2(x - 3 )] / (x - 3)(x - 2) = 8/x

[By taking LCM ]

[x - 2 + 2x - 6 ] / (x² - 2x - 3x - 6) = 8/x

(3x - 8) / (x² - 5x - 6) = 8/x

x (3x - 8) = 8(x² - 5x - 6)

3x² - 8x = 8x² - 40x - 48  

3x² - 8x² - 8x + 40x + 48 = 0

-5x² + 32x  + 48 = 0

5x² - 32x - 48 = 0

[-20 × - 12 = 240 & -20 -12 = -32]

5x² - 20x -12x - 48 = 0

5x(x - 4) -12(x - 4) = 0

(5x -12) (x - 4) = 0

5x - 12 = 0   or  x - 4 = 0  

5x = 12  or  x = 4

x = 12/5  or x = 4  

Hence, the roots of the quadratic equation 1/(x - 3)  +  2/(x - 2)  = 8/x  are  12/5   &  4 .

 

HOPE THIS ANSWER WILL HELP YOU….

step by step explanation

FACTORIZATION METHOD : We first write the given quadratic polynomial as product of two linear factors by splitting the middle term and then equate each factor to zero to get desired roots of given quadratic equation.