Signing you in…

Vieta's theorem

If x1x_1 and x2x_2 are roots of the monic quadratic x2+px+q=0x^2+px+q=0, then x1+x2=−px_1+x_2=-p, x1x2=qx_1x_2=q. For ax2+bx+c=0ax^2+bx+c=0 (a≠0a\neq0) divide by aa first, or use x1+x2=−bax_1+x_2=-\frac{b}{a}, x1x2=cax_1x_2=\frac{c}{a}.
Vieta's formulas work both ways: from roots to coefficients, and from coefficients to checking roots
Integer roots are often found from divisors of the constant term
When sum and product are obvious, you can build the equation without the discriminant formula
Sum and product of the roots.
Vieta: sum and product of roots
x2−7x+12=0x^2-7x+12=0
=x1+x2=7, x1x2=12=x_1+x_2=7,\ x_1x_2=12
−p=7, q=12-p=7,\ q=12
Content is available with subscription.
Get full access to all courses on the platform for one year with a single payment.
Unlike other platforms that charge per course, here you get everything for one price, and after one year of use there will be no automatic charge for the following year.