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Standard XII

Mathematics

Location of Roots when Compared with a constant 'k'

Let S be the ...

Question

Let S be the set of values of 'a' for which 2 lie between the roots of quadratic equation $x^{2} + (a + 2) x - (a + 3) = 0$ . Then S is given by

(-∞, -5)

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(5, ∞)

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(-∞, -5]

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[5, ∞)

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Solution

The correct option is A (-∞, -5)
Solution : $x^{2} + (a + 2) x - (a + 3) = 0$
$f (2) < 0$
$4 + 2 (a + 2) - (a + 3) < 0$
$a + 5 < 0$
$a < - 5$
$a \in (- \infty, - 5)$

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Let S be the set of values of 'a' for which 2 lie between the roots of quadratic equation x2+(a+2)x−(a+3)=0. Then S is given by

The correct option is A (-∞, -5)Solution : x2+(a+2)x−(a+3)=0 f(2)<0 4+2(a+2)−(a+3)<0 a+5<0 a<−5 a∈(−∞,−5)

Let S be the set of values of 'a' for which 2 lie between the roots of quadratic equation $x^{2} + (a + 2) x - (a + 3) = 0$ . Then S is given by

The correct option is A (-∞, -5)
Solution : $x^{2} + (a + 2) x - (a + 3) = 0$
$f (2) < 0$
$4 + 2 (a + 2) - (a + 3) < 0$
$a + 5 < 0$
$a < - 5$
$a \in (- \infty, - 5)$