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Standard XIII

Mathematics

Graph of Quadratic Expression

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

(- \infty, - 5)

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(5, \infty)

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(- \infty, - 5]

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[5, \infty)

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Solution

The correct option is A $(- \infty, - 5)$
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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(a – 5) $x^{2}$ – 2ax + (a – 4) = 0, a $\neq$ 5 such that
P : All values of ‘a’ for which the product of roots of given quadratic equation is positive.
Q : All values of ‘a’ for which the product of roots of given quadratic equation is negative.
R : All values of ‘a’ for which the product of real roots of given quadratic equation is positive.
S : All values of ‘a’ for which the roots of given quadratic are real.
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Let P, Q, R, S and T are five sets about the quadratic equation

(a – 5) $x^{2}$ – 2ax + (a – 4) = 0, a $\neq$ 5 such that

P : All values of ‘a’ for which the product of roots of given quadratic equation is positive.

Q : All values of ‘a’ for which the product of roots of given quadratic equation is negative.

R : All values of ‘a’ for which the product of real roots of given quadratic equation is positive.

S : All values of ‘a’ for which the roots of given quadratic are real.

T : All values of ‘a’ for which the given quadratic equation has complex roots.

Which statement is correct regarding sets, P, Q and R ?

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