Question

Change equation into root form

Answer 1

The roots of the quadratic equation
`\(2x^2 - 9x + 7\)` are
`\(x = (7)/(2)\)` and
`\(x = 1\)`. In root form, the equation is
`\(f(x) = 2(x - (7)/(2))(x - 1)\).`

To write the equation
`\( f(x) = 2x^2 - 9x + 7 \)` in root form, we first need to factorize the quadratic expression. However, the given quadratic does not factor easily, so we can use the quadratic formula:

The quadratic formula for a quadratic equation
`\( ax^2 + bx + c = 0 \)` is given by:

`\[ x = (-b \pm √(b^2 - 4ac))/(2a) \]`

In the case of
`\( f(x) = 2x^2 - 9x + 7 \),` where
`\( a = 2 \), \( b = -9 \), and \( c = 7 \),` the roots can be found using the quadratic formula:

`\[ x = (9 \pm √((-9)^2 - 4(2)(7)))/(2(2)) \]`

Simplifying further:

`\[ x = (9 \pm √(81 - 56))/(4) \]`

`\[ x = (9 \pm √(25))/(4) \]`

So, the roots are:

`\[ x = (9 + 5)/(4) = (14)/(4) = (7)/(2) \]`

and

`\[ x = (9 - 5)/(4) = (4)/(4) = 1 \]`

Therefore, the roots in root form are
`\( x = (7)/(2) \)` and
`\( x = 1 \),` and the equation in root form would be:

`\[ f(x) = 2(x - (7)/(2))(x - 1) \]`