Sum of the roots of a quadratic equation is doubie their product. Fin

1.	Sum of the roots of a quadratic equation is doubie their product. Fin kif the equation is x2 -4kx +k+ 3 0
Answer» Let α and β are the roots of 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 x²αβ = (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 Like my answer if you find it useful!

Sum of the roots of a quadratic equation is doubie their product. Fin kif the equation is x2 -4kx +k+ 3 0

Answer»

Let α and β are the roots of 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 x²αβ = (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

Like my answer if you find it useful!