Question

SECTION A
Find the discriminant of the equation (x + 3)3 = 4 - x + x3​

Answer 1

Given to find Discriminant of Equation :-

(x + 3)³ = 4 - x + x³

Solution:-

Discriminant of Quadratic equation is given by b²-4ac

First Lets simplify the given Equation

(x + 3)³ = 4 - x + x³

Expand (x + 3)³ It is in form of (a + b)³ =a³ + b³ +3ab (a + b)

(x + 3)³ = x³ + (3)³ + 3(x)(3) (x+3)

(x +3)³ = x³ + 27 + 9x(x +3)

(x + 3)³ = x³ + 27 + 9x² + 27x

= x³ + 9x² + 27x + 27

(x + 3)³ = 4 - x + x³

x³ + 9x² + 27x + 27 = x³-x + 4

Tranpose all terms to RHS

x³ + 9x² + 27x + 27 - x³ + x -4 =0

x³ - x³ +9x² +27x +x 27-4 =0

9x² + 28x + 23 = 0

Lets find Discriminant

D = b²- 4ac

• a = 9
• b = 28
• c = 23

D = (28)²-4(9)(23)

D =784 - 828

D = -44

So, Discriminant of Quadratic equation is -44