Question

Find the discriminant of -18p=p^2+81

Answer 1

Step-by-step explanation:

`\sf - 18p = p^2+81`

Moving all the expression to the Left side of the equation,

`\sf -18p + p^2 - 81 = 0`

To find the discriminant of the above equation we can simply use the Quadratic formula.

The discriminant formula of a quadratic equation
`\sf ax^2 + bx + c = 0 \: is \: (d = b^2 - 4ac )`

Where d represents the discriminant

a, b and c are the coefficient of the above equation,

p^2, here coefficient of p² is a = 1

-18p, here coefficient of p is b = -18

81, here the number is constant so coefficient is c = 81.

So simply by substituting the value of a, b and c in the above discriminant formula we get,

`\sf d = b^2 - 4ac`

`\sf d = (-18)^2 - (4 * 1 * 81)`

`\sf d = 324 - 324`

`\sf d = 0`

Therefore, The discriminant of 18p = p² + 81 is 0.

Answer 2

0 (zero)

Explanation:

To find the discriminant of the quadratic equation -18p = p² + 81, we first need to rewrite the equation in standard form, which is of the form ax² + bx + c = 0.

`\begin{aligned}-18p&=p^2+81\\p^2+81&=-18p\\p^2+81+18p&=-18p+18p\\p^2 + 18p + 81 &= 0\end{aligned}`

Compare the coefficients of the rewritten quadratic equation with the standard form:

• a = 1
• b = 18
• c = 81

The discriminant of a quadratic equation in the form ax² + bx + c = 0 is given by the formula:

`\boxed{\textsf{Discriminant} = b^2 - 4ac}`

Substitute the values of a, b, and c into the formula:

`\begin{aligned}\textsf{Discriminant} &= (18)^2 - 4(1)(81)\\&=324-4(81)\\&=324-324\\&=0\end{aligned}`

Therefore, the discriminant of the given quadratic equation is zero.