Week 7-Precalc11 – Yi's Blog

Discriminant is a formula that we use to determine the root of a quadratic polynomial. The standard form of it is $b^2-4ac$ .

There are three causes here:

$b^2-4ac>0$ , the quadratic polynomial has two distinct roots

$b^2-4ac=0$ , the quadratic polynomial has two equal roots

$b^2-4ac<0$ , the quadratic polynomial has no real roots

Ex:Find how many roots of following polynomials.

$5x^2+x-2,b^2-4ac=1^2-4\cdot5\cdot(-2)=1+40=41>0$ so that this polynomial has two distinct roots.

$x^2+4x+4,b^2-4ac=4^2-4\cdot1\cdot4=16-16=0$ so that this polynomial has two equal roots.

$5x^2+x+2,b^2-4ac=1^2-4\cdot5\cdot2=1-40=-39<0$ so that this polynomial has no real roots.

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