Question

Determine the value of p for which the quadratic equation 4x^2 - 3px + 9 = 0 has distinct real roots​

Answer 1

equation is 4x^2-3px+9=0
according to given condition
Δ=0
comparing with ax^2-3px+9=0
therefore,
a=4 , b=-3p and c=9
Δ=b^2-4ac
=(-3p)^2-4x4x9
=9p^2-144

but. Δ=0
9p^2-144=0
9p^2=144
(3p)^2=144
3p=√144
3p=12
p=12/3
p=4

Answer 2

Given:

A quadratic equation 4x² - 3px + 9 = 0 has equal roots.

To Find:

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

Solution:

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

1. The given quadratic equation is 4x² - 3px + 9 = 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 ) = $\sqrt[2]{b^2-4ac}$.  

=> For real roots D > 0.  

3. Substitute the values in the above formula,  

=>  D > 0,  

=> √[(3p)² - 4(4)(9)] > 0,

=> 9p² -144 > 0,

=> 9p² > 144,

=> p² > 16

=> p > ±4.

=> p > + 4 (OR) p < -4.

Therefore, the values of p are p > ± 4.