Question

Without solving the equation, determine the nature of the roots of x2 - 2 x - 8 = 0.

Answer 1

Evaluate using the discriminant (the part of the quadratic equation under the square root sign) b²-4ac
In your equation, a=1, b=(-2), and c=(-8)...substitute their values into the discriminant:
(-2)²-4(1)(-8)
4+32 = 36

The value is positive, therefore the equation has two real roots.
It's a perfect square (√36=6) so the roots are rational
Answer: two real, rational roots

(If the result was a negative number, the system would have two irrational roots. If the result was zero, the system would have a double root (one value repeated twice - when graphed, the vertex of the parabola falls on the x-axis)∨