What is the nature of a quadratic equation having a discriminate equal to 0?

Answer 1

Hi Sammie! It means that the roots are rational and equal. This is because the square root of the discriminant is added then subtracted from -b to get the 2 roots, so if you add 0 and subtract 0 you get the same answer. And 0 is a rational number.

Answer 2

formidable question: a quadratic equation has equivalent roots while discriminant is 0. B^2 - 4AC = 0 subsequently, A = ok, B = -5, and C = ok we could desire to clean up (-5)^2 - 4(ok)(ok) = 0 25 - 4k^2 = 0 -4k^2 = -25 ok^2 = 25/4 ok = +/- 5/2 question a million: enable's locate the roots employing quadratic formula x = (-(-5) +/- sqrt((-5)^2 - 4(3)(2))) / (2*3) x = (5 +/- sqrt(25 - 24)) / 6 x = (5 +/- sqrt(a million)) / 6 x = (5 +/- a million) / 6 x = (5+a million) / 6 or x = (5-a million) / 6 x = a million or x = 2/3 answer: x = a million or x = 2/3 question 2: there is no ok in this equation so which you won't be able to locate it question 3: practice that the discriminant is 0. locate B^2 - 4AC the place A = 2, B = -4, C = 3. (-4)^2 - 4(2)(3) sixteen - 24 -8 that may no longer 0. So it does not have equivalent roots. question 4: locate the roots first and then their sum and product. x = (-(5) +/- sqrt((-5)^2 - 4(2)(-4))) / (2*2) x = (5 +/- sqrt(25 - -32)) / 4 x = (5 +/- sqrt(fifty seven)) / 4 x = (5 + sqrt(fifty seven)) / 4 or x = (5 - sqrt(fifty seven)) / 4 Sum: [(5 + sqrt(fifty seven)) / 4] + [(5 - sqrt(fifty seven) / 4] = [5 + sqrt(fifty seven) + 5 - sqrt(fifty seven)] / 4 = 10/4 = 5/2 Product: [(5 + sqrt(fifty seven)) / 4] * [(5 - sqrt(fifty seven) / 4] = [25 - 5sqrt(fifty seven) + 5sqrt(fifty seven) - fifty seven] / sixteen = -32/sixteen = -2 question 5: could desire to locate x and x + a million such that x^2 + (x + a million)^2 = 25 x^2 + x^2 + 2x + a million = 25 2x^2 + 2x + a million = 25 2x^2 + 2x - 24 = 0 x^2 + x - 12 = 0 (x + 4)(x - 3) = 0 x = -4 or x = 3 we'd like useful numbers so we are able to forget approximately approximately x = -4 x = 3. Then x + a million = 4 answer: 3,4

Answer 3

It means the equation has 2 equal roots.
Geometrically, it means the graph of the equation
is tangent to the x-axis.
Example: x²-2x+1 =0.
Discriminant = 4-4=0.
Both roots are 1
and this parabola is tangent to the x-axis at x = 1.

Answer 4

The quadratic equation ax^2 + bx +c = 0 has discriminant

b^2 - 4ac.

Its called the discriminant because

Discriminant positive means "two distinct real roots"
Discriminant negative means "two complex roots"
Discriminant zero means "two identical real roots"

So the discriminant because it discriminates the types of roots of the quadratic equation.

Answer 5

The formula for the roots of a quadratic equation is

-b +- sqrt(b^2 - 4ac)/2a

If the discriminate is 0 (sqrt(b^2 -4ac) = 0) then there is one and only one real root, namely, -b/2a.

HTH

Charles

Answer 6

There is a one double root, which means the graph is tangent to the x-axis. It also means that the quadratic can be expressed as the square of a monomial.

Answer 7

It has one root, -b/2a. (techinically, a double root.)
graphically, it would look like a parabola with its vertex touching the x axis at ((-b/2a).,0)

Answer 8

Both roots are equal. Root = -b/2a

Answer 9

The answer is undifined. If the discriminate is zero.