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