Let p, q ∈ 1,2,3,4 . The number of equation of form p x2+q x+1=0 having real roots is k. Then find k.

Question

Let p, q ∈ 1,2,3,4 . The number of equation of form p x2+q x+1=0 having real roots is k. Then find k. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Equation will have roots if p2 ≥ 4 q If q=1, then p2 ≥ 4 q for p=2,3 and 4 q=3, then p2 ≥ 4 q for p=4 q=2, then p2 ≥ 4 q for p=3 and p=4 q=4, then p2 ≥ 4 q for p=4 Total 7 possibilities.

Q. Let $p, q \in {1, 2, 3, 4}$ . The number of equation of form $p x^{2} + q x + 1 = 0$ having real roots is $k$ . Then find $k$ .

Equation will have roots if $p^{2} \geq 4 q$
If $q = 1$ , then $p^{2} \geq 4 q$ for $p = 2, 3$ and $4$
$q = 3$ , then $p^{2} \geq 4 q$ for $p = 4$
$q = 2$ , then $p^{2} \geq 4 q$ for $p = 3$ and $p = 4$
$q = 4$ , then $p^{2} \geq 4 q$ for $p = 4$
Total $7$ possibilities.

Q. Let p,q∈{1,2,3,4}. The number of equation of form px2+qx+1=0 having real roots is k. Then find k.

Equation will have roots if p2≥4q If q=1, then p2≥4q for p=2,3 and 4 q=3, then p2≥4q for p=4 q=2, then p2≥4q for p=3 and p=4 q=4, then p2≥4q for p=4 Total 7 possibilities.

Q. Let $p, q \in {1, 2, 3, 4}$ . The number of equation of form $p x^{2} + q x + 1 = 0$ having real roots is $k$ . Then find $k$ .

Equation will have roots if $p^{2} \geq 4 q$
If $q = 1$ , then $p^{2} \geq 4 q$ for $p = 2, 3$ and $4$
$q = 3$ , then $p^{2} \geq 4 q$ for $p = 4$
$q = 2$ , then $p^{2} \geq 4 q$ for $p = 3$ and $p = 4$
$q = 4$ , then $p^{2} \geq 4 q$ for $p = 4$
Total $7$ possibilities.