Cubic Equation Formula

Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols (currently expressed as Latin and Greek letters) represent quantities with no set values, known as variables, in introductory algebra. In mathematics, equations express relationships between variables in the same way that sentences describe relationships between specific words.

What is an equation?

Equations are mathematical statements that comprise two algebraic equations on opposite sides of an ‘equal to (=)’ sign. It depicts the equality link between the expression written on the left side and the expression written on the right side. L.H.S = R.H.S (left hand side = right hand side) appears in every mathematical equation. Equations can be used to calculate the value of an unknown variable that represents an unknown quantity. 

Cubic equation Formula

A cubic equation, often known as a cubic polynomial, is a polynomial of degree three. Cubic equations have at least one real root and up to three real roots. A cubic equation’s roots can also be imaginary, but at least one must be real.

The standard form of a cubic equation with variable x is,

ax³ + bx² + cx + d = 0, where a ≠ 0

Here, a, b and c are the coefficients and d is the constant.

The cubic equation formula may also be used to calculate the cubic equation’s curve. The use of a cubic equation formula to represent a cubic equation is highly useful in locating the cubic equation’s roots. A polynomial of degree n will have n zeros or roots.

Example: Find a cubic equation in x for the values of a, b, c and d as 2, –3, –4, 7 respectively.

 We have, a = 2, b = –3, c = –4 and d = 7

The general form of a cubic equation is, ax³ + bx² + cx + d = 0.

So, the required equation is,

P(x) = 2x³ + (–3)x² + (–4)x + 7

= 2x³ – 3x² – 4x + 7

Sample Problems

Question 1. Find a cubic equation in x for the values of a, b, c and d as 6, –5, 0, 2 respectively.

Solution:

 We have, a = 6, b = –5, c = 0 and d = 2

The general form of a cubic equation is, ax³ + bx² + cx + d = 0.

So, the required equation is,

P(x) = 6x³ + (–5)x² + 0x + 2

= 6x³ – 5x² + 2

Question 2. Find a cubic equation in y for the values of a, b, c and d as 2, –3, 1, 5 respectively.

Solution:

 We have, a = 2, b = –3, c = 1 and d = 5

The general form of a cubic equation is, ax³ + bx² + cx + d = 0.

So, the required equation is,

P(x) = 2y³ + (–3)y² + 1y + 5

= 2y³ – 3y² + y + 5

Question 3. Find a cubic equation in z for the values of a, b, c and d as 9, 0, 1, 0 respectively.

Solution:

 We have, a = 9, b = 0, c = 1 and d = 0

The general form of a cubic equation is, ax³ + bx² + cx + d = 0.

So, the required equation is,

P(x) = 9z³ + 0x² + 1z + 0

= 9z³ + z

Question 4. Find a cubic equation in x for the values of a, b, c and d as 6, 0, 0, 9 respectively.

Solution:

 We have, a = 6, b = 0, c = 0 and d = 9

The general form of a cubic equation is, ax³ + bx² + cx + d = 0.

So, the required equation is,

P(x) = 6x³ + 0x² + 0x + 9

= 6x³ + 9

Question 5. Find a cubic equation in y for the values of a, b, c and d as –3, –4, 0, 0 respectively.

Solution:

 We have, a = –3, b = –4, c = 0 and d = 0

The general form of a cubic equation is, ax³ + bx² + cx + d = 0.

So, the required equation is,

P(x) = (–3)y³ + (–4)y² + 0y + 0

= –3y³ – 4y²

Question 6. Find a cubic equation in z for the values of a, b, c and d as 7, 0, –1, 0 respectively.

Solution:

 We have, a = 7, b = 0, c = –1 and d = 0

The general form of a cubic equation is, ax³ + bx² + cx + d = 0.

So, the required equation is,

P(x) = 7z³ + 0z² + (–1)z + 0

= 7z³ – z