The number of points p- q such that p- q -1-2-3-4 and the equation p x2-q x-1-0 has real roots isA- 7B- 8C- 9D- None of these

The correct option is A 7 px^2+qx+1=0 has real roots if q^2 4p ≥ 0 or q^2 ≥ 4p Since p, q ϵ{1,2,3,4} The required points are(1,2), (1,3),(1, 4), (2,3),(2,4),(3 ...

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Standard XII

Mathematics

Perpendicular Distance of a Point from a Plane

The number of...

Question

The number of points (p, q) such that $p, q ϵ {1, 2, 3, 4}$ and the equation $p x^{2} + q x + 1 = 0$ has real roots is

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None of these

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Solution

The correct option is A
7

$p x^{2} + q x + 1 = 0$ has real roots if $q^{2} - 4 p \geq 0 o r q^{2} \geq 4 p$

$S i n c e p, q ϵ {1, 2, 3, 4}$

The required points are(1,2), (1,3),(1, 4), (2,3),(2,4),(3,4),(4,4)

So the required number is 7

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The number of points (p, q) such that p,q ϵ {1,2,3,4} and the equation px2+qx+1=0 has real roots is

The correct option is A 7 px2+qx+1=0 has real roots if q2−4p≥0 or q2 ≥4p Since p,qϵ{1,2,3,4} The required points are(1,2), (1,3),(1, 4), (2,3),(2,4),(3,4),(4,4) So the required number is 7

The number of points (p, q) such that $p, q ϵ {1, 2, 3, 4}$ and the equation $p x^{2} + q x + 1 = 0$ has real roots is

The correct option is A
7

$p x^{2} + q x + 1 = 0$ has real roots if $q^{2} - 4 p \geq 0 o r q^{2} \geq 4 p$

$S i n c e p, q ϵ {1, 2, 3, 4}$

The required points are(1,2), (1,3),(1, 4), (2,3),(2,4),(3,4),(4,4)

So the required number is 7