How many real number solutions does the equation have? 0 = -7x^2 + 6x + 3

one solution
two solutions**
no solution

How many real number solutions does the equation have? 0 = 2x^2 - 20x + 50
one solution
two solutions
no solution**

Find the discriminant: D=b^2-4ac

if D>0, there are two real number solutions
if D=0, there is one solution
if D<0, there are no solutions

Using the quadratic equation: ax^2 + bx +c, insert the values into the discriminant.

1) -7x^2 + 6x + 3

D=(6)^2 - 4(-7)(3)
=36+84
=120>0
Therefore, there are 2 real number solutions.

2) 2x^2 - 20x + 50

D=400-400
= 0
Therefore, there is one solution.

For the second one I thought it was negative?

(-20)^2 - 4(2)(50) =
- 400 - 400 = -800?

thanks soo much everyone!! :3

sorry ... b^2 = (-20)^2 = (-20)(-20) = 400 not -400

-400 is -20^2 = -b^2 because exponents are done first.

Well, it seems like the first equation is having a party and inviting two solutions over! They must be real numbers, of course. As for the second equation, it seems to be feeling a bit lonely with no solutions showing up to the party. It's just not as popular, I guess.

To determine the number of real number solutions for a quadratic equation in the form of ax^2 + bx + c = 0, we can use the discriminant.

For the equation 0 = -7x^2 + 6x + 3, the quadratic coefficients are a = -7, b = 6, and c = 3.

The discriminant is given by the formula D = b^2 - 4ac. Plugging in the values, we have D = (6)^2 - 4(-7)(3) = 36 + 84 = 120.

If the discriminant is positive (D > 0), then the quadratic equation has two distinct real number solutions.
If the discriminant is zero (D = 0), then the quadratic equation has one real number solution (a repeated root).
If the discriminant is negative (D < 0), then the quadratic equation has no real number solutions.

In this case, for the equation 0 = -7x^2 + 6x + 3, the discriminant is D = 120, which is positive. Therefore, this equation has two real number solutions.

For the equation 0 = 2x^2 - 20x + 50, the quadratic coefficients are a = 2, b = -20, and c = 50.

The discriminant is D = (-20)^2 - 4(2)(50) = 400 - 400 = 0.

Since the discriminant is equal to zero, 0 = 2x^2 - 20x + 50 has one real number solution (a repeated root).

Therefore, the correct answers are:
- The equation 0 = -7x^2 + 6x + 3 has two solutions.

- The equation 0 = 2x^2 - 20x + 50 has one solution.

#1 ok

#2 nope. the polynomial is 2(x-5)^2
always check the discriminant. For this one, it is zero, indicating one repeated root.