First slide

Theory of expressions

Question

The values of a for which one root of the equation $x^{2} - (a + 1) x + a^{2} + a - 8$ $= 0$ exceeds 2 and the other is lesser than 2, are given by

Moderate

A

$a > 3$
B

$9 < a < 10$
C

$- 2 < a < 3$
D

None of these

Solution

he given equation is $x^{2} - (a + 1) x + a^{2} + a - 8$ $= 0$ …. ( 1 )
If the roots of the given equation are
real and distinct D $>$ o $\Rightarrow$ $3 a^{2} + 2 a - 33 < 0$ $\Rightarrow$ a $\in$ ( $\frac{- 11}{3}$ ,3)………(1)
and f(2) less than 0
$\Rightarrow 4 - (a + 1) 2 + a^{2} + a - 8 < 0$
so a $\in$ (-2,3)……. ……..(2)
from 1&2 we get a $\in$ (-2,3)

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