Question

The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35.find the equation

Answer 1

Answer:

x² - 5x + 6 = 0

Step-by-step explanation:

2 + 3 = 5 and 2³ + 3³ = 8 + 27 = 35

So the roots of the quadratic equation are 2 and 3

So the quadratic equation will be

(x - 2)(x - 3) = 0

x² - 5x + 6 = 0

Answer 2

Answer:

p(x) = k[x² - 5x + 9]

Step-by-step explanation:

Let the two roots be ∝ and β.

Given:

∝ + β = 5

∝³ + β³ = 35

Solution:

∝³ + β³ = 35    (Given)

⇒ (∝ + β)(∝² - ∝β + β²) = 35     (a³ + b³ = (a+b)(a² - ab + b²))

⇒ 5(∝² + β² - ∝β) = 35              (∝ + β = 5)

⇒ (∝ + β)² - 2∝β - ∝β = 7        (∝² + β² = (∝ + β)² - 2∝β)

⇒ (5)² - 3∝β = 7

⇒ 25 - 3∝β = 7

⇒ 3∝β = 25 - 7

⇒ 3∝β = 18

⇒ ∝β = 6

p(x) = k[x² - (∝ + β) + ∝β]

p(x) = k[x² - 5x + 6]