Discriminant

[chaput]

Hi there, could someone please help me workout this question:
Find the value(s) of p for which:
A) px^2 −6x + p = 0 has one solution

B)2x^2 −4x + 3 = p has two solutions

Thank you!

[Opengangs]

Hey!

So if you recall the discriminant, there will lie one solution if and only if the discriminant is equal to 0.
Likewise, there will lie no solutions if and only if the discriminant is less than 0.
And there will lie 2 solutions if and only if the discriminant is greater than 0.

So using this condition, we can solve for \(p\).

To get you started, consider the discriminant of some quadratic: \( ax^2 + bx + c = 0 \).
The discriminant can be found by the formula: \( b^2 - 4ac \).

So, for (a), we see that:


Could you use the same idea for (b)?

[chaput]

Hey!

So if you recall the discriminant, there will lie one solution if and only if the discriminant is equal to 0.
Likewise, there will lie no solutions if and only if the discriminant is less than 0.
And there will lie 2 solutions if and only if the discriminant is greater than 0.

So using this condition, we can solve for \(p\).

To get you started, consider the discriminant of some quadratic: \( ax^2 + bx + c = 0 \).
The discriminant can be found by the formula: \( b^2 - 4ac \).

So, for (a), we see that:


Could you use the same idea for (b)?

Hey there,
Thanks so much for the help! But i am still having slight trouble with B ://

[Opengangs]

Hey there,
Thanks so much for the help! But i am still having slight trouble with B ://

Sure, so this will work if our left equation is equal to 0. This is essentially because the discriminant tells us how many roots an equation may have.

To get it in the form we want, subtract p from both sides.



This is of the form we want our equation to be in, so you could then use the discriminant to find what values of \( p \) we could have that will give us 2 solutions.

[chaput]

Sure, so this will work if our left equation is equal to 0. This is essentially because the discriminant tells us how many roots an equation may have.

To get it in the form we want, subtract p from both sides.



This is of the form we want our equation to be in, so you could then use the discriminant to find what values of \( p \) we could have that will give us 2 solutions.

Thank you very much for the help!!