> > Please help ASAP Find the value of the discriminant and describe the number and type of roots.

# Please help ASAP Find the value of the discriminant and describe the number and type of roots.

## x2 + 5x + 6 = 0 x2 - 8x +16 = 0 3x2 - 5x + 6 = 0 6x2 -x - 12 = 0 3x...

127 Views

### Please help ASAP Find the value of the discriminant and describe the number and type of roots.

x2 + 5x + 6 = 0 x2 - 8x +16 = 0 3x2 - 5x + 6 = 0 6x2 -x - 12 = 0 3x2 - 8x + 2 = 0

$$ax^2+bx+c=0\\\\the\ discriminant\ \Delta=b^2-4ac\\\\If\ \Delta > 0\ then\ two oots\\If\ \Delta=0\ then\ one oot\\If\ \Delta 0-two ational oots\\\\x^2-8x+16=0\\a=1\ b=-8\ c=16\\\Delta=(-8)^2-4\cdot1\cdot16=64-64=0-one ational oot\\\\3x^2-5x+6=0\\a=3\ b=-5\ c=6\\\Delta=(-5)^2-4\cdot3\cdot6=25-72=-47< 0-no eal oots$$ $$6x^2-x-12=0\\a=6\ b=-1\ c=-12\\\Delta=(-1)^2-4\cdot6\cdot(-12)=1+288=289-two ational oots\\\\3x^2-8x+2=0\\a=3\ b=-8\ c=2\\\Delta=(-8)^2-4\cdot3\cdot2=64-24=40-two\ irrational oots$$ ================================================== $$A ational oots\ if\ \sqrt{\Delta}\in\mathbb{N}\\\\An\ irrational oots\ if\ \sqrt\Deltaotin\mathbb{N}$$