Question

given that 2x2 + 5x + k is the value of p(x) hence find teh value of k​

Answer 1

Answer:

Refer to attachment ✌️

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Answer 2

Answer:

α and β are the zeroes of the polynomial

⇒ p(x) = 2x² + 5x + k

• Sum of the zeroes = α + β = -(coefficient of x) / (coefficient of x2) = -5/2
• Product of the zeroes = αβ = -(constant term) / (coefficient of x2) = k/2

⇒ α² + β² + αβ = 21/4

⇒ (α + β)2 - αβ = 21/4

⇒ (-5/2)2 - k/2 = 21/4

⇒ 25/4 - k/2 = 21/4

⇒ k/2 = 25/4 - 21/4

⇒ k/2 = 1

⇒ k = 2

• Therefore, The Value of k is 2.