please help!!!?

Question

describe the roots of the equation x^2 +8x-9=0
a: imaginary
b:2 rational roots
c:two equal roots
d:2 irrational roots

Also, x^2-3y^2=9 is that a circle, hyperbola line or ellipse?

Answer 1

For any equation of the form ax^2+bx+c=0, you can use the quadratic equation to find the roots:

x = (-b +/- sqrt(b^2 - 4*a*c))/(2*a)

For your equation a=1, b=8, and c=-9. I don't have a calculator with me, but (b^2-4*a*c) will be a positive number, so the roots won't be imaginary (e.g. won't include any square roots of negative numbers), and also because (b^2-4*a*c) will not be zero, it will have two roots. As to rational or irrational, that depends on whether (b^2-4*a*c) is a perfect square or not (don't have a calculator, argh).

As to your second question, circles have the form (a^2)*x^2+(a^2)*y^2=r^2, where r/a is the radius. Ellipses are similar, (a^2)*x^2+(b^2)*y^2=r^2, where a is not equal to b. Your formua has a minus sign, so it fits neither of the two formulas I mentioned (a^2 and b^2 must be positive), so by process of elimination (assuming that circle, ellipse, and hyperbola are your only choices), it's a hyperbola.

Answer 2

DO YOUR OWN HOME WORK.....