Question

Determine the values of p for which the given quadratic equation has distinct real roots for x square - 3p x + 9 equal to zero

Answer 1

Answer:

The quadratic has distinct real roots when p < -2 and when p > 2.

Step-by-step explanation:

A quadratic ax² + bx + c has distinct real roots when its discriminant Δ=b²-4ac is greater than 0.

So here,

x² - 3px + 9 has distinct real roots

<=> (3p)² - (4)(9) > 0

<=> 9p² > (4)(9)

<=> p² > 4

<=> p < -2  or  p > 2

Answer 2

the condition for that is,

D>0 & a>0

where D=b²-4ac

where b=3p , a=1 & c=9

now D>0

(3p)² - 4(1)(9)>0

9p² - 9*4>0

p' > 0

p>2 and p<-2

p ∈ (-∞,-2)∪(2,∞)