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

p x 2 + q x + 1 = 0 has real roots ⇒ q 2 − 4 p ≥ 0 ⇒ 4 p ≤ q 2 ⇒ ( 1 , 2 ) ( 1 , 3 ) ( 1 , 4 ) ( 2 , 3 ) ( 2 , 4 ) ( 3 , 4 ) ( 4 , 4 ) ∴ number of points = 7

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MathematicsFunctionsMiscellaneous/MixedMedium2 minQB

MathematicsMediuminteger

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

Answer:

Solution:

$p x^{2} + q x + 1 = 0$ has real roots $\Rightarrow q^{2} - 4 p \geq 0 \Rightarrow 4 p \leq q^{2}$ $\Rightarrow (1, 2) (1, 3) (1, 4) (2, 3) (2, 4) (3, 4) (4, 4)$ ∴ number of points $= 7$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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