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# Linear and quadratic systems — Harder example

Watch Sal work through a harder Linear and quadratic systems problem.

## Want to join the conversation?

• In a quadratic equation of form
ax^2+bx+c=0
the product of their roots is c/a.
So you dont need to solve them to find the product of two roots
• We could just use Vieta Theorem to find the product of the roots. It's quite more convenient.
• Another one is that the sum of the solutions of a quadratic in that form is -b/a.
• The SAT answer grid does not have an option for a negative answer. why is the answer here negative?
• An answer on the SAT won't be negative if you won't be able to answer it. :)
• you could have solved the question without even factorizing/solving the equation as the coefficient of X^0 that is -2 is already the product of the two X co-ordinates.
• What do you mean by the `coefficient of X^0`? The constant term in the equation?
• How do you know when to substitute and when to set the equations equal to each other? For a simple problem like this where both equations equal Y I understand, but what if they don't?
• math is so delicious i love it
• What are the values of:
(1) 0^0
(2) infinity^0 ?
Are they equal to 1 too?
• 0^0 and infinity^0 both are equal to infinity.
a^0 = 1 if only a<>0
• how do we know when to use the quadratic formula?
like why didnt we just do 2x^2+11x-6 =0
a.b = -12
a+b = 11