If 3 is a root of (x^{2} + kx - 24 = 0), it is also a root o... | MATH - CONDITION FOR COMMON ROOTS, QUADRATIC EXPRESSIONS AND POSITION OF ROOTS | SolveeIt

If 3 is a root of $x^{2} + kx - 24 = 0$ , it is also a root of

$x^{2} + 5x + k = 0$

$x^{2} - 5x + k = 0$

$x^{2} - kx + 6 = 0$

$x^{2} + kx + 24 = 0$

Answer

$x^{2} - kx + 6 = 0$

Explanation

Equation $x^{2} + kx - 24 = 0$ has one root as 3,

⇒ $3^{2} + 3k - 24 = 0$ ⇒ $k = 5$

Put $x = 3$ and $k = 5$ in option

Only (3) gives the correct answer i.e. ⇒ $3^{2} - 15 + 9 = 0$

⇒ $0 = 0$

Question: If 3 is a root of \(x^{2} + kx - 24 = 0\), it is also a root of...