Question

Solve the quadratic equation x² –  3(x + 3) = 0; Give your answer correct to two significant figures.

Answer 1

Given: x² –  3(x + 3) = 0

x² – 3x – 9 = 0

Comparing x² – 3x – 9 = 0 with ax² + bx + c = 0, we get

a = 1, b = –3, c = –9

We know,

∴ `x = (-b +- sqrt(b^2 - 4ac))/(2a)`

`=> x = (-(-3) +- sqrt((-3)^2 - 4(1)(-9)))/(2(1))`

`=> x = (3 +- sqrt(9 + 36))/2`

`=> x = (3 +- sqrt45)/2`

`=> x = (3 +- sqrt(9 xx 5))/2`

`=> x = (3 +- 3sqrt5)/2`

`=> x = (3 + 3sqrt5)/2` or `x = (3 - 3sqrt5)/2`

`=> x  = (3 + 3 xx 2.236)/2` or `x = (3 - 3 xx 2.236)/2`

`=> x = (3 + 6.708)/2` or `x = (3 - 6.708)/2`

`=> x = 9.708/2` or `x = (-3.708)/2`

`=>` x = 4.85 or x = –1.85

`=>` x = 4.9 or x = –1.9