Question

When the following quadratic equation is written in general form, what is the value of "c"?

-3/4x^2 + 2 = 0

Answer 1

The value of c is -8

Explanation:

Given

`(-3)/(4) x^2 + 2 = 0`

Required

The value of c, when written in a general form.

The general form of a quadratic equation is written as ax² + bx + c = 0

To get the general form of
`(-3)/(4) x^2 + 2 = 0`, we start by converting the fraction to whole number.

This is done by multiplying both sides of the equation by the denominator of the fraction (4)

Multiply through by 4; This gives us

`4 * (-3)/(4) x^2 + 4 * 2 = 4 * 0`

`-3x^2 + 8 = 0`

From the general form of a quadratic equation, ax² + bx + c = 0 , it'll be observed that a is positive and by comparison a = -3 (in
`-3x^2 + 8 = 0`)

So, we have to convert -3 to a positive integer by multiplying both sides of the equation by -1. This gives

`-1 * -3x^2 + -1 * 8 = -1 * 0`

`3x^2 - 8 = 0`

Writing
`3x^2 - 8 = 0` in a more general form, we have

`3x^2 + 0x - 8 = 0`

By comparing ax² + bx + c = 0 to
`3x^2 + 0x - 8 = 0`

a = 3

b = 0

c = -8

Hence, the value of c is -8