Solve the equation x^2 + 3x – 4 = 0 in two ways.  

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We have to solve the quadratic equation x^2 + 3x – 4 = 0.

One way to do this is by factorization.

x^2 + 3x – 4 = 0

=> x^2 + 4x – x – 4 =0

=> x(x+4) -1(x+4) = 0

=> (x – 1)(x + 4) =0

...

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We have to solve the quadratic equation x^2 + 3x – 4 = 0.

One way to do this is by factorization.

x^2 + 3x – 4 = 0

=> x^2 + 4x – x – 4 =0

=> x(x+4) -1(x+4) = 0

=> (x – 1)(x + 4) =0

=> x can be 1 and -4

Another way to solve this is to use the formula for roots of a quadratic equation which is [–b+ sqrt(b^2 – 4ac)] / 2a and –b - sqrt(b^2 – 4ac)] / 2a

substituting the values we get

x1 = [-3 + sqrt(9 + 16)]/ 2

=>( -3 + 5)/2 = 2/2 = 1

x2 = [-3 - sqrt(9 + 16)]/ 2

=>( -3 - 5)/2 = -8/2 = -4

The roots of the equation are x = 1 and x = -4.

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