Question

The zeroes of the polynomial 3x² + 8x − 3 are ______.

Options

• `1/3, 3`

• `1/3, -3`

• `(-1)/3, 3`

• `(-1)/3, -3`

Answer 1

The zeroes of the polynomial 3x² + 8x − 3 are `\underlinebb(1/3, -3)`.

Explanation:

The general form of a quadratic equation is:

ax² + bx + c = 0

The roots of the equation are given by the quadratic formula:

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

For the polynomial 3x² + 8x − 3 = 0,

a = 3, b = 8, c = −3

`"x" = (-8 +- sqrt(8^2 - 4(3)(-3)))/(2(3))`

`"x" = (-8 +- sqrt(64 + 36))/6`

`"x" = (-8 +- sqrt100)/6`

`"x" = (-8 +- 10)/6`

`"x" = (-8  + 10)/6`

= `2/6`

=`1/3`

`"x" = (-8 - 10)/6`

= `(-18)/6`

= −3

The zeroes of the polynomial 3x² + 8x − 3 are x = `1/3` and x = −3.