First slide

Theory of equations

Question

The coefficient of x in the equation $x^{2} + px + q = 0$ was taken as
$17$ in place of $13$ , its roots were found to be $- 2 and - 15$ .
The roots of the original equation are

Moderate

A

$3, 10$
B

$- 3, - 10$
C

$- 5, - 18$
D

None of these

Solution

Let the equation (in correctly written form) be $x^{2} + 17 x + q = 0$ .
Roots are $- 2, - 15$ . So 30=q,
so correct equation is $x^{2} + 13 x + 30 = 0 .$
Hence roots are $- 3, - 10$ .

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