Question

Find the roots of the quadratic equation by using the quadratic formula in the following:

`1/2x^2 - sqrt(11)x + 1 = 0`

Answer 1

The quadratic formula for finding the roots of quadratic equation

ax² + bx + c = 0, a ≠ 0 is given by,

x = `(-b +- sqrt(b^2 - 4ac))/(2a)`

∴ x = `(-(-sqrt(11)) +- sqrt((-sqrt(11))^2 - 4(1/2)(1)))/(2(1/2))`

= `(sqrt(11) +- sqrt(9))/1`

= `sqrt(11) +- 3`

= `3 + sqrt(11), -3 + sqrt(11)`