Find p such that px^2-12x+4=0 has only one solution.
Thank you!!!
the answer 9
Well, let's put on our funny glasses and solve this equation in a hilarious way! To find when this quadratic equation has only one solution, we need to make sure that the discriminant, b^2 - 4ac, is equal to zero. So, let's plug in the values from your equation, which gives us 12^2 - 4p(4) = 0. Now, let me do some math here... hmm... carry the laughter... divide by the fun factor... Eureka! The 144 simplifies, and we are left with -16p = 0! So, to solve it, we divide by -16 and get p = 0! Ta-da! The value of p that makes the equation have one solution is "zero," just like the number of fruit at a clown picnic. Enjoy!
To find the value of p such that the equation px^2 - 12x + 4 = 0 has only one solution, we need to use the discriminant.
The discriminant is given by the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = p, b = -12, and c = 4.
For a quadratic equation to have only one solution, the discriminant must be equal to zero (Δ = 0). Therefore, we can set up the equation:
Δ = (-12)^2 - 4(p)(4) = 0
Simplifying, we have:
144 - 16p = 0
To find the value of p, we need to solve this equation for p.
Subtracting 144 from both sides:
-16p = -144
Dividing by -16:
p = 9
Therefore, for the equation px^2 - 12x + 4 = 0 to have only one solution, p must be equal to 9.
To find the value of p such that the quadratic equation px^2 - 12x + 4 = 0 has only one solution, we need to use the discriminant, which is the expression b^2 - 4ac in the quadratic formula.
In this case, the quadratic equation is in the form ax^2 + bx + c = 0, where a = p, b = -12, and c = 4.
Since we want the equation to have only one solution, the discriminant should be equal to zero, since a discriminant of zero indicates that the quadratic equation has only one real solution.
Therefore, we have:
Discriminant = (-12)^2 - 4(p)(4) = 144 - 16p
To find the value of p, we set the discriminant equal to zero and solve for p:
144 - 16p = 0
16p = 144
p = 144/16
Simplifying, we find that p = 9.
So, to make the quadratic equation px^2 - 12x + 4 = 0 have only one solution, the value of p should be 9.
In quadratic equation:
a x ^ 2 + b x + c
value D = b ^ 2 - 4ac is called the discriminant.
When Discriminant is zero we get just one real solution.
p x ^ 2 - 12 x + 4 = 0
In this case :
a = p , b = - 12 , c = 4
D = b ^ 2 - 4 a c =
( - 12 ) ^ 2 - 4 * p * 4 =
144 - 16 p = 0 Add 16 p to both sides
144 - 16 p + 16 p = 0 + 16 p
144 = 16 p Divide both sides by 16
144 / 16 = p
9 = p
p = 9
p x ^ 2 - 12 x + 4 = 0
become:
9 x ^ 2 - 12 x + 4 = 0
By the way the solution is x = 2 / 3