value of discriminant of each equation, decide how many different real-number roots the equation has, and?

Question

1.) x^2+7x+9=0

a.discriminant 13 1 real root with porabla intersecting at the x axis at only 1 point.
b.discimanant 13 with 2 real roots ,with the porablaintercecting the x axis at two points.
c.discriminant 13 there are two real roots with porabla intersecting the x axis only at one point(13,0)


2.)2x^2+5x+7=0

a.diriminant -31there are two real roots with porabla intersecting the x axis at two places
b.dicriminant -31 two real negative roots with the porabla intersecting th x axis at two places
c.disciminant is-31 no real roots,with porabla not intersecting at the xais at all.


thank you so much

Answer 1

For a quadratic in standard form P(x)=ax²+bx+c,

the discriminant D is given by: D = b²-4ac.

• If D>0, P(x) has two real roots, and its graph crosses the x-axis twice.

• If D=0, P(x) has one real root, and its graph touches the x-axis once.

• If D<0, P(x) has no real roots, and its graph doesn't cross the x-axis.



1) Because the discriminant is positive, there are 2 real roots.

The parabola crosses the x-axis at two points.



2) Because the discriminant is negative, there are no real roots.

The parabola lies entirely above the x-axis, and never crosses it.

Answer 2

Check out my Math Variety blog posts about how to find the discriminant in a quadratic equation. I have an explanation of what it is, practice problems, and solutions. http://mathvariety.blogspot.com/2009/04/discriminant-in-quadratic-equation.html

http://mathvariety.blogspot.com/2009/05/discriminant-in-quadratic-equation.html

http://mathvariety.blogspot.com/2009/05/discriminant-in-quadratic-equation_11.html



For the first one, the discriminant is positive, so there are two real roots with the parabola intersecting the x-axis at two points. The answer is b.



For the second one, the discriminant is negative, so there are no real roots and the parabola does not intersect the x-axis at all. The answer is c.

Answer 3

the only help that i can give is that the formula for the discriminant is (b^2 - 4ac) / 4a. its very hard to solve them. and i can't assure you that i can give the right answers but the formula is 100% correct.