Question

Solve by using the quadratic formula.
3psquared+7p+2=0

Answer 1

`\large\boxed{x=-2\ or\ x=-(1)/(3)}`

Explanation:

The quadratic formula of a quadratic equation

`ax^2+bx+c=0\\\\x=(-b\pm√(b^2-4ac))/(2a)`

We have the equation:

`3p^2+7p+2=0\to a=3,\ b=7,\ c=2`

Substitute:

`b^2-4ac=7^2-4(3)(2)=49-24=25\\\\√(b^2-4ac)=√(25)=5\\\\x_1=(-7-5)/(2(3))=(-12)/(6)=-2\\\\x_2=(-7+5)/(2(3))=(-2)/(6)=-(1)/(3)`

Answer 2

-1/3,-2

Explanation:

The quadratic formula is [-b±√(b^2-4ac)]/2a. In this equations 3p^2 is a, 7p is b, and 2 is c.

Then just plug in the numbers.

[-7±√((-7^2)-4(3)(2)]/2(3)

[-7±√(25)]/6

(-7+5)/6 and (-7-5)/6

-1/3 and -2 are the answers, if you plug these numbers into the original equation, you find that they equal 0 which means that they work.