How many real number solutions? −7x2+6x+3=0

2 Answers
Bill Jorgensen
May 28, 2018

discriminant = 120

two real irrational solutions.

Explanation:

−7x2+6x+3

To solve this use the discriminant:

ax2+bx+c

discriminant =b2−4ac

=62−4⋅−7⋅3

=36−(−84)

=120

discriminant > 0: two real solutions.

discriminant = 0: one real solutions, bounce or double solution.

discriminant < 0: two imaginary solutions.

discriminant = perfect square: solution is rational

Douglas K.
May 28, 2018

d=120, therefore, there are two distinct real roots.

Explanation:

One can find the number of real solutions of a quadratic of the form, y=ax2+bx+c, by computing the determinant, d=b2−4ac

If d<0, then there are no real roots.
If d=0, then there is one real root (called a repeated root).
If d>0, then there are two distinct real roots:

Given: −7x2+6x+3=0

d=62−4(−7)(3)

d=120, therefore, there are two distinct real roots.

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