Find the value of p for which the quadratic equation px2+6x+1=0 has real roots

Question

Find the value of p for which the quadratic equation px²+6x+1=0 has real roots

Answer 1

Given equation, px²+6x+1=0

Here, a = p, b = 6, c = 1

Since roots are real,

So, b² - 4ac ≥ 0

(p)² - 4 x 6 x 1 ≥ 0

p² – 24 ≥ 0

p² ≥ 24

p ≥ ±√24

p ≥ ±2√6

The value of p so that the equation px²+6x+1=0 has real roots is p ≥ 2√6 or p ≥ -2√6.