Question

if alpha and beta equal to 3 and Alpha Cube + beta cube equal to 9 find the quadratic equation whose roots are alpha and beta​

Answer 1

Solution:

We have been given that a + ß = 3 and a³ +ß³ = 9.

• a + ß = 3 ....(i)
• a³ +ß³ = 9 ...(ii)

Solve Equation (ii):

• a³ +ß³ = 9

⇒ a³ + b³ = ( a +b)(a²-ab+b²)

⇒ a³ + b³ = ( a+b)[(a+b)² -2ab -ab ]

⇒ 9 = (3)[(3)² -3ab ]

⇒ 9 = 3[9 - 3ab]

⇒ 9 = 27 -9ab

⇒ 9 + 27 = -9ab

⇒ 36 = -4ab

⇒ ab = -4

We have to find Quadratic Equation which zeros are a and ß.

f(x) = x² -(a+ß)x + aß

⇒ x² - (3)x + (-4) = 0

⇒ x² - 3x - 4 = 0

Therefore, Required Quadratic Equation is x² - 3x - 4 = 0.