Question

If a and b are the zeroes of 2x² + 5 x + k such that a^{​​​​​​2}+b^{​​​​​​2}+ ab = 21/4, find k

Answer 1

Sol:
α and β are the zeroes of the polynomial f(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
hope you understand this