First slide

Theory of equations

Question

$If p, q \in {1, 2, 3, 4}, the number of equations of the form p x^{2} + q x + 1 = 0 having real roots is$

Moderate

A

7
B

8
C

15
D

9

Solution

For real roots, we must have
$\begin{array}{l} Disc \geq 0 \Rightarrow q^{2} - 4 p \geq 0 \Rightarrow q^{2} \geq 4 p \\ If p = 1, then q^{2} \geq 4 p \Rightarrow q^{2} \geq 4 \Rightarrow q = 2, 3, 4 \\ p = 2, then q^{2} \geq 4 p \Rightarrow q^{2} \geq 8 \Rightarrow q = 3, 4 \\ p = 3, then q^{2} \geq 4 p \Rightarrow q^{2} \geq 12 \Rightarrow q = 4 \\ p = 4, then q^{2} \geq 4 p \Rightarrow q^{2} \geq 16 \Rightarrow q = 4 \end{array}$
$Thus, we see that there are 7 cases.$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App