Question

6. For what values of p, the equation 3x2 + 2px + 5 = 0 has equal roots?​

Answer 1

Step-by-step explanation:

Refer the attachment ❤️

Answer 2

Step-by-step explanation:

Given:-

the equation 3x^2 + 2px + 5 = 0

To find:-

For what values of p, the equation

3x^2 + 2px + 5 = 0 has equal roots?

Solution:-

Given equation is 3x^2 + 2px + 5 = 0

On comparing with the standard quadratic equation ax^2+bx+c = 0

Then we have

a = 3

b= 2p

c= 5

We know that

ax^2+bx+c = 0 has equal roots if the discriminant of the equation must be zero

The discriminant of ax^2+bx+c = 0 is b^2-4ac

According to the given problem

D=b^2-4ac = 0

=>(2p)^2-4(3)(5) = 0

=>4p^2 - 60 = 0

= >4p^2 = 60

=> p^2 = 60/4

=>p^2 = 15

=>p = ±√15

Therefore, p = √15 or -√15

Answer:-

The value of p for the given problem is √15 and -√15

Used formulae:-

• The discriminant of ax^2+bx+c = 0 is b^2-4ac
• the standard quadratic equation ax^2+bx+c = 0