First slide

Theory of equations

Question

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

Moderate

A

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

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

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

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

Solution

Equation $x^{2} + kx - 24 = 0$ has one root is 3
$\Rightarrow 3^{2} - 3 k - 24 = 0 \Rightarrow k = 5$
Put $x = 3 and k = 5$ in options, only option (3) gives the correct answer.

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