Question

the quadratic equation 2x²+px+3=0 has two equal roots if p=?​

Answer 1

Answer:

answer is + or - √24

Step-by-step explanation:

Given equation has equal roots,

So, its Discriminant, D=0

D=p²-5(2)(3)=0

p²=24

p= + or -√24

Answer 2

Given:

A quadratic equation 2x²+px+3=0 has equal roots.

To Find:

The value of k such that the equation has equal roots is?

Solution:

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

1. The given quadratic equation is 2x²+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 equal roots D = 0.  

3. Substitute the values in the above formula,  

=> D = 0,  

=> √[(p)² - 4(2)(3)] = 0,

=> p² -24 = 0,

=> p² = 24,

=> p = √(24),

=> p = ±2√6.

Therefore, the values of p are ±2√6.