Question

solve the following quadratic equation x^2 -7x+3=0.give your answer correct to two decimal place.

Answer 1

Answer:

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Answer 2

x = 6.45, 0.46 (correct to 2D)

Solve by quadratic formula :

The given equation is

x² - 7x + 3 = 0

Comparing the above equation with the general equation ax² + bx + c = 0, we get

a = 1, b = - 7 and c = 3

Therefore the required solution is

x = {- b ± √(b² - 4ac)}/2a

or, x = {7 ± √(49 - 12)}/2

or, x = (7 ± √37)/2

or, x = 6.45138, 0.45862

or, x = 6.45, 0.46 (correct to 2D)

Solve by completing the square method :

The given equation is

x² - 7x + 3 = 0

or, x² - (2 * x * 7/2) + (7/2)² - (7/2)² + 3 = 0

or, (x - 7/2)² - 37/4 = 0

or, (x - 7/2)² - {(√37)/2}² = 0

or, {x - 7/2 + (√37)/2} {x - 7/2 - (√37)/2} = 0

Either x - 7/2 + (√37)/2 = 0 or, x - 7/2 - (√37)/2 = 0

∴ x = 7/2 - (√37)/2, x = 7/2 + (√37)/2

= 0.45862 = 6.45138

≈ 0.46 ≈ 6.45 (correct to 2D)

This is the required solution.

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