Question

Which of the following polynomials does not have real roots? Will fan and give medal!!
A.)12x^2-17x-7
B.) x^2+x+2
C.) x^2+5x+6
D.) x^2+x-2

Answer 1

for polynomial \(ax^2+bx+c\) we look at the determinant \(b^2-4ac\)
if \(b^2-4ac\ge0\) then we will have real roots
if \(b^2-4ac< 0\) we will not.

Answer 2

try to factor them, and the one you can't factor does not have real roots

Answer 3

don't do that, the point of this question is to look at the determinant.

@sbookdog the point of looking at the determinant, is that one does NOT need to factor the quadratic to answer these type of questions, it is so much easier to figure out if \((-17)^2-4(12)(-7)\ge 0\)

Answer 4

you don't even need to do the math, this is a positive number plus a positive number.... so the first one has real roots.

Answer 5

Thank-you zzr0ck3r!