Question

Whats this? `x^2+16x=61`

Answer 1

This is a trinomial

Explanation:

This trinomial can be solved using the quadratic equation.

Answer 2

`color(maroon)(x = -8 + 5sqrt5, -8- 5sqrt5`

Explanation:

`x^2 + 16x = 61`

A trinomial is a 3 term polynomial. For example, 5x2 − 2x + 3 is a trinomial.

`x^2 + 16x - 61 = 0` `" is a quadratic equation which has two values for variable 'x'"`

`"Degree of equation " color(crimson)(2), " no. of terms " color(crimson)(3, " trinomial")`

Standard form of quadratic equation is `a x^2 + bx + c = 0`

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

`:. a = 1, b = 16, c = -61`

`x = (-16 +- sqrt(16^2 - 4*1 * -61)) / (2*1)`

`x = (-16 +- sqrt(256 + 244)) / 2`

`x = (-16 +- sqrt(500)) / 2 = -8 +- sqrt125`

`color(maroon)(x = -8 + 5sqrt5, -8- 5sqrt5`

Answer 3

x-intercepts: `(-8+5sqrt5,0)` and `(-8-5sqrt5,0)`

Approximate x-intercepts: `(3.18,0)` and `(-19.8,0)`

Explanation:

Solve:

`x^2+16x=61`

Subtract `61` from both sides of the equation.

`x^2+16x-61=0` is a quadratic equation in standard form, set equal to `0` rather than `y` so we can solve for the x-intercepts:

`ax^2+bx+c=0`,

where:

`a=1`, `b=16`, and `c="-61`

To solve for `x`, use the quadratic formula.

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

Plug in the known values and solve.

`x=(-16+-sqrt(16^2-4*1*-61))/(2*1)`

Simplify.

`x=(-16+-sqrt(500))/2`

Prime factorize `500`.

`x=(-16+-sqrt(2xx2xx5xx5xx5))/2`

`x=(-16+-sqrt(2^2xx5^2xx5))/2`

Apply rule: `sqrt(a^2)=a`

`x=(-16+-2xx5sqrt5)/2`

`x=(-16+-10sqrt5)/2`

Simplify.

`x=-8+-5sqrt5`

`x=-8+5sqrt5, -8-5sqrt5`

x-intercepts: `(-8+5sqrt5,0)` and `(-8-5sqrt5,0)`

Approximate x-intercepts: `(3.18,0)` and `(-19.8,0)`

graph{y=x^2+16x-61 [-14.02, 8.48, -7.83, 3.42]}