Question

If alpha and beta are the zeros of the polynomial 2x2+5x+k, find k such that (alpha)2+(beta)2+(alpha)*(beta)=24

Answer 1

: α and β are zeroes of polynomial
 2x² + 5x + k

THEN 
α+β = -5/2 , αβ = k/2

⇒ (α+β)² = (-5/2)²

⇒ α²+ β²+ 2αβ = 25/4

⇒ α²+ β²+ αβ+ αβ = 25/4

⇒ 24 + k/2=25/4

⇒ k/2 = 25/4 - 24

⇒ k/2 = 25/4 - 96/4

⇒ k/2 = -71/4

⇒k = -71/4 * 2

⇒k = -71/2

Answer 2

Answer:

-71/2

Step-by-step explanation:

α and β are zeroes of polynomial

 2x² + 5x + k

THEN 

α+β = -5/2 , αβ = k/2

⇒ (α+β)² = (-5/2)²

⇒ α²+ β²+ 2αβ = 25/4

⇒ α²+ β²+ αβ+ αβ = 25/4

⇒ 24 + k/2=25/4

⇒ k/2 = 25/4 - 24

⇒ k/2 = 25/4 - 96/4

⇒ k/2 = -71/4

⇒k = -71/4 * 2

⇒k = -71/2