Math Question- For what value will the equation have only 1 answer.?

Question

For what values(s) of k will the equation 3x^2-kx+5 have exactly one solution?

Can someone please explain to me how you go about solving this?

Answer 1

Consider the quadratic formula. The discriminant is the part that gives two answers. So to have only one answer, the discriminant, b^2 - 4ac, has to be 0. So you want k^2 - 4x3x5 = 0. So k^2 = 60 and k = +/- sqrt 60.

In general, you want the discriminant to be 0. So if they give you something like this on the test, whether k is in the position of a or b or c, put what you know in the form b^2 - 4ac = 0 and solve.

Answer 2

wHere is the equation at all ? You have given only an expression. So presume this expression is equal to zero.

This being a second degree equation, it will normally have two solutions. It will have single solution if you can write the expression as a square of a first degree monomial. i.e. if you can express given 3x^2 - kx + 5 as a perfect square i.e. like (ax + b)^2 .....
3x^2 - kx + 5 = (ax + b)^2 = a^2.x^2 + 2abx + b^2
Equating the coefficients of similar terms,
a^2 = 3 ...... a = Sqrt 3
b^2 = 5 ...... b = Sqrt 5
k = -2ab = -2 (sqrt 3)(sqrt 5) = -2 Sqrt(15)

Answer 3

For 3x^2 - kx + 5 to have only one root, 3x^2 - kx + 5 must be a "perfect square".
Since (ax - b)^2 = a^x^2 -2abx + b^2
a ≡ √3
b ≡ √5, and
-2ab ≡ -2√3√5, and
k ≡ 2√15

Answer 4

ok...well to solve this you have to understand that the equation will have only answer when the equation is equal to zero...if it is less than zero than there are no solutions, and greater than zero means two solutions. so, simply set the equation 3x^2-kx+5=0 and solve the equation for k using a quadratic formula and you will have the answer that the other person probably gave you.

Answer 5

3x^2-kx+5, b/c the highest power of this equation is 2, so it must has 2 solutions, it might repeat, so the ppl thought it's only one solution.
if you want to find the repeat root, you must have to perfect the square. the number with out x is 5 only. so you have to think about n x n = 5, so n is "5 root" and what m x m is 3, so m is "3 root". rewrite the equation. ((root 3)x + (root 5))^2
let's solve for k, use foil,
(root 3 x)(root 3 x) +2(root 3)(x)(root 5) + (root 5)(root 5)
= 3x^2 + (root 15)x + 5
so k is equal to (root 15)
and the solution for x is -(root 5)/(root 3) or -(root 15)/3

Answer 6

Set the discriminant equal to zero!

So k^2-4*3*5=0 and solve for k:

k=+ or - 2*sqrt(15)....two values for k

Answer 7

you get only 1 answer when the quadratic equation portion b^2 - 4ac = 0
b = -k
a = 3
c = 5
Substituting:
(-k)^2 - (4*3*5) = 0
k^2 - 60 = 0
k^2 = 60
k = sqrt 60 = 7.745966

Answer 8

3x² - kx + 5
delta = k² - 4.3.5
delta = k² - 60
k equal or more 2√15
::

Answer 9

Ans :2*sqrt(15)

Answer 10

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