Question

Sum of the roots of a quadratic equation is double their product.Find k if equation is
x-4kr+k+3-0. quadratic equation ​

Answer 1

Answer:

quadratic equation x² - 4kx + k + 3 = 0

∴sum of roots = - coefficient of x²/coefficient of x

α + β = -(-4k)/1 = 4k

Product of roots = constant/coefficient of x²

αβ = (k + 3)/1 = (k + 3)

A/C to question,

sum of roots = 2 × product of roots

(α + β ) = 2αβ

⇒4k = 2(k + 3)

⇒ 4k = 2k + 6

⇒ 4k - 2k = 6

⇒ 2k = 6

⇒ k = 3

Hence, answer is k = 3

Step-by-step explanation:

quadratic equation x² - 4kx + k + 3 = 0

∴sum of roots = - coefficient of x²/coefficient of x

α + β = -(-4k)/1 = 4k

Product of roots = constant/coefficient of x²

αβ = (k + 3)/1 = (k + 3)

A/C to question,

sum of roots = 2 × product of roots

(α + β ) = 2αβ

⇒4k = 2(k + 3)

⇒ 4k = 2k + 6

⇒ 4k - 2k = 6

⇒ 2k = 6

⇒ k = 3

Hence, answer is k = 3