Question

for what value of p , the equation 3x2+px+3=0 has real roots?

Answer 1

Answer:

p > ±6

Step-by-step explanation:

p∧2 - 36 >0

p∧2 > 36

p > √36

p > ±6

Answer 2

Given:

A quadratic equation 3x² + px + 3 = 0 has equal roots.

To Find:

The value of p such that the equation has real roots is?

Solution:

The given problem can be solved using the concepts of quadratic equations.    

1. The given quadratic equation is 3x² + px + 3 = 0.  

2. For an equation to have equal roots the value of the discriminant is 0,  

=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,  

=> Discriminant ( D ) = $\sqrt{b^2-4ac}$.  

=> For real roots D >= 0.  

3. Substitute the values in the above formula,  

=>  D >= 0,  

=> √[(p)² - 4(3)(3)] ≥ 0,

=> k² -36 ≥ 0,

=> p² ≥ 36,

=> p ≥ +6 (OR) p ≤ -6.

Therefore, the values of p are p ≥ +6 (OR) p ≤ -6.