Question

If a and b are zeroes of the quadratic polynomial 2x2 + 3x - 6, then find the values of (i) a2+b2 (ii) a3+b3 (iii) a− b (iv) a2 /b+ b2/a (v) a2+2

Answer 1

Step-by-step explanation:

hope it helps

.

.

.

.

.

.

.

plzzzz give thnx and Mark as brainlist

Answer 2

Answer:

Refer the given solution.

Given:

2x² + 3x - 6

To Find:

(i) α² + β²  

(ii) α³+β³  

(iii) α − β

(iv) α²/β + β²/α

Step-by-step explanation:

Quadratic equation is  2x² + 3x - 6

a = 2, b = 3, c = -6

sum of roots:

(α + β) = -b/a = -3/2

product of roots:

(αβ) = c/a == -6/2 = -3

(i) α² + β² = (α + β)² - 2αβ

⇒ (-3/2)² - 2(-3)

⇒ 9/4 + 6

⇒ (9+24)/4

⇒ 33/4

(ii) α³+β³ = (α + β)³ - 3αβ(α + β)

⇒ (-3/2)² - 3(-3)(-3/2)

⇒ 9/4 - 27/2

⇒(9 - 54)/4

⇒ -45/4

(iii) α − β = √ (α + β)² - 4αβ

⇒ √(-3/2)² - 4(-3)

⇒ √(9/4 + 12)

⇒ √(9 + 48)/4

⇒ √ (57/4)

⇒ (√57)/2

(iv) α²/β + β²/α = ( α³+β³)/αβ

⇒(-45/4)/-3

⇒ 45/12

⇒ 15/4

#SPJ2