Question

Express the given equation in the standard form and then find its roots by factorisation method (2x-3) (x-2) + (2x-7)(x-4)=5 1/2

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

(2x-3)(x-2) + (2x-7)(x-4) = 5 1/2

2x^2 - 4x - 3x + 6 + 2x^2 -8x - 7x + 28 =  11/2

4x^2 - 22x + 34 = 11/2

2(4x^2 - 22x + 34) = 11

8x^2 - 44x + 68 = 11

8x^2 - 44x + 57 = 0 [Standard Form]

 Discriminant is $\sqrt{b^{2} - 4ac }$

= $\sqrt{112}$

Since discriminant is irrational we should use quadratic formula

-b + D      =     $\frac{44 + 4\sqrt{7} }{16} , \frac{44 - 4\sqrt{7} }{16}$ =  $\frac{11 + \sqrt{7} }{4} , \frac{11 - \sqrt{7} }{4}$

  2a