Question

2. Solve the following quadratic equations using quadratic formula

Answer 1

(x - 1)/(x + 1) + (x - 3)/(x - 4) = 10/3

[(x - 1)(x - 4) + (x - 3)(x + 1)]/(x + 1)(x - 4) = 10/3

3[x² - 4x - x + 4 + x² + x - 3x - 3] = 10(x² - 4x + x - 4)

3[2x² - 7x + 1] = 10(x² - 3x - 4)

6x² - 21x + 3 = 10x² - 30x - 40

4x² - 9x - 43 = 0
where, a = 4 , b = -9 , c = -43

D = b² - 4ac
D = (-9)² - 4(4)(-43)
D = 81 + 688
D = 769
√D = √769

quadratic formula = $\bold{\frac{-b +_-\sqrt{D}}{2a}}$

X = $\bold{\frac{-(-9) +_-\sqrt{769}}{2(4)}}$

X = $\bold{\frac{9 +-\sqrt{769}}{8}}$

X = $\bold{\frac{9 + \sqrt{769}}{8}}$

X = $\bold{\frac{9 - \sqrt{769}}{8}}$

Answer 2

Compare 4x² - 9x - 43 = 0 with

ax² + bx + c = 0 , We get

a = 4 , b = -9 , c = -43 ,

Discreminant ( D ) = b² - 4ac

= ( -9 )² - 4 × 4 × ( -43 )

= 81 + 688

= 769

D = 769

By Quadratic Formula :

x = [ -b ± √D ]/2a

x = [-(-9) ± √769 ]/( 2 × 4)

x = [ 9 ± √769 ]/8

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