Question

6x^2-9x +2=0 solve the quadratic equation using the quadratic formula

Answer 1

The roots of
`6 x^(2)-9 x+2=0` are
`(9+√(33))/(4), (9-√(33))/(4)`

SOLUTION:

Given, quadratic equation is
`6 x^(2)-9 x+2=0` --- eqn (1)

We need to find the roots of given quadratic equation using quadratic formula.

Quadratic formula for general quadratic equation
`a x^(2)+b x+c=0` is
`X=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

Here, for eqn (1) a = 6, b= -9 and c = 2

`X=\frac{-(-9) \pm \sqrt{(-9)^(2)-4 *6 * 2}}{2 x 2}`

`X=(9 \pm √(81-48))/(4)`

`\begin{array}{l}{X=(9 \pm √(33))/(4)} \\ {X=(9+√(33))/(4), (9-√(33))/(4)}\end{array}`

Hence the roots of
`6 x^(2)-9 x+2=0` are
`(9+√(33))/(4), (9-√(33))/(4)`