First slide

Theory of equations

Question

$The coefficient of x in the equation x^{2} + p x + q = 0 was wrongly written as 17 in place of 13 and the roots thus$
$found was - 2 and - 15 . Then the roots of the correct equation are$

Moderate

A

-3, 10
B

-3, -10
C

3, -10
D

None of these

Solution

$Correct equation is x^{2} + 13 x + q = 0 - - - - (1)$
$Incorrect equation is x^{2} + 17 x + q = 0 - - - - - (2)$
$Given, roots of equation (1) are - 2 and - 15$
$So, product of roots of incorrect equation, q = (- 2) (- 15) = 30$
$From (1), correct equation is$
$x^{2} + 13 x + 30 = 0 ∴ x = - 3, - 10$

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