-7x^2+6x+3=0
why are there 2 solutions for this one?
Please and thank you so much
There are two solutions to every quadratic equation.
If you cannot easily see how to factor the expression, then you can always use the quadratic formula. In this case,
x = (-6±√(36+84))/-14 = (3±√30)/7
to find the nature of the roots (solutions)
you can solve it with the quadratic formula (or factoring)
or ... find the discriminant ... b^2 - 4 a c
There are 2 solutions because a graph of the function crosses the x-axis
twice.
To find the solutions of a quadratic equation like -7x^2 + 6x + 3 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation -7x^2 + 6x + 3 = 0, we can identify that a = -7, b = 6, and c = 3. Substituting these values into the quadratic formula, we get:
x = (-6 ± √(6^2 - 4(-7)(3))) / (2(-7))
x = (-6 ± √(36 + 84)) / (-14)
x = (-6 ± √120) / (-14)
x = (-6 ± √(4 * 30)) / (-14)
x = (-6 ± 2√30) / (-14)
Simplifying further, we have:
x = (-3 ± √30) / (-7)
Now we have two possible solutions:
Solution 1: x = (-3 + √30) / (-7)
Solution 2: x = (-3 - √30) / (-7)
This is why there are two solutions for the given equation.