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Standard XII

Mathematics

Nature of Roots

Sum of the ro...

Question

Sum of the roots of the equation $(x - 2)^{2} - 2 | x - 2 | - 15 = 0$ , is:

4

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Solution

The correct option is A $4$
$| x - 2 | = t$
$t^{2} - 2 t - 15 = 0$
$(t - 5) (t + 3) = 0$
$t^{2} - 3$
$t^{2} + 5$
$t < 0$
$∴$ $t = 5$
$x - 2 = 5$
$x = 7$
$x - 2 = - 5$
$x = - 3$
$∴$ sum of roots $= 7 - 3 = 4$

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Sum of the roots of the equation (x−2)2−2|x−2|−15=0, is:

The correct option is A 4|x−2|=tt2−2t−15=0(t−5)(t+3)=0t2−3t2+5t<0∴ t=5x−2=5x=7x−2=−5x=−3∴ sum of roots =7−3=4

Sum of the roots of the equation $(x - 2)^{2} - 2 | x - 2 | - 15 = 0$ , is:

The correct option is A $4$
$| x - 2 | = t$
$t^{2} - 2 t - 15 = 0$
$(t - 5) (t + 3) = 0$
$t^{2} - 3$
$t^{2} + 5$
$t < 0$
$∴$ $t = 5$
$x - 2 = 5$
$x = 7$
$x - 2 = - 5$
$x = - 3$
$∴$ sum of roots $= 7 - 3 = 4$