discriminant- finding it and findingunequal real roots (1 Viewer)

[Born Dancer]

ok so im doing a past trial paper and i really cant do the discriminant questions. im stuck on the following:

1) write down the discriminant of 2x^2 - 3x + k

for this... do i just use the formula?? b^2 - 4ac?? i got 9-8k

2) for what value of k does 2x^2 - 3x + k = 0 have unequal real roots?

am stuck on this question.. the only thing i think im sposed to use is alpha and beta???

please help!!

 

[FinalFantasy]

ok so im doing a past trial paper and i really cant do the discriminant questions. im stuck on the following:

1) write down the discriminant of 2x^2 - 3x + k

for this... do i just use the formula?? b^2 - 4ac?? i got 9-8k

2) for what value of k does 2x^2 - 3x + k = 0 have unequal real roots?

am stuck on this question.. the only thing i think im sposed to use is alpha and beta???

please help!!

1. delta=9-4(2)k=9-8k so u are rite
2.for 2x^2 - 3x + k = 0 to have unequal real roots,
delta>0
9-8k>0
9>8k
k<9\8

 

[who_loves_maths]

Originally Posted by FinalFantasy
2.for 2x^2 - 3x + k = 0 to have unequal real roots,
delta>0
9-8k>0
9>8k
k<9\8

nice FF, but Morning Glory said it must be done using just alpha or beta...

Morning Glory, x = -b/2a gives you the vertex of the parabola. now, in order for the parabola to have two distinct real roots, it has to cut the x-axis at two places, ie. no double root, OR, the vertex must NOT TOUCH the x-axis:

-b/2a = 3/4 ; ie. at x = 3/4, y = 2(3/4)^2 - 3(3/4) + k ;

since the parabola is concave UP, then:

y < 0 -----> 2(3/4)^2 - 3(3/4) + k < 0 -----> k < 9/8

hope this provides an alternative solution for you
{although, FinalFantasy's method is the faster one, so use that whenever you can, unless the question otherwise specifies.}

 

[who_loves_maths]

btw, Morning Glory, if by alpha and beta you mean the roots of the equation, then the vertex, in terms of the roots, is: x = (alpha + beta)/2 .

 

[FinalFantasy]

hey.. but she said "the only thing i think im sposed to use is alpha and beta???"
she "think" she suppose to use alpha and beta
she didn't say u "must"
hehe, unless it's said somewhere else and i didn't c it @_@

 

[Slidey]

ok so im doing a past trial paper and i really cant do the discriminant questions. im stuck on the following:

1) write down the discriminant of 2x^2 - 3x + k

for this... do i just use the formula?? b^2 - 4ac?? i got 9-8k

2) for what value of k does 2x^2 - 3x + k = 0 have unequal real roots?

am stuck on this question.. the only thing i think im sposed to use is alpha and beta???

please help!!

Unequal roots distinct roots. As it said real, we can exclude complex ones, so we want when the discriminant is > 0, as FF did.

Why? If the discriminant is zero, than the solutions to the quadratic equation are of the form x=(-b+sqrt(0))/a, thus x is only one value. However, if the discriminant (the bit under the square root) is greater than zero, you get two distinct values for x, so two unequal roots.

 

[who_loves_maths]

Originally Posted by FinalFantasy
hey.. but she said "the only thing i think im sposed to use is alpha and beta???"
she "think" she suppose to use alpha and beta
she didn't say u "must"
hehe, unless it's said somewhere else and i didn't c it @_@

yea my fault for putting that "must" word in there. but plz don't get me wrong or take offense, i was just offering an alternative solution for Morning_Glory in light of using alpha and beta and not necessarily the discriminant.

your method is perfectly fine, but i was trying to give as much help as i can to Morning_Glory since she was curious about using alpha and beta to doing the problem ... and like i offered in my explanation to Morning_Glory, using alpha and beta is unnecesarily time-consuming compared to using the discriminant like you did:

Originally Posted by who_loves_maths
hope this provides an alternative solution for you
{although, FinalFantasy's method is the faster one, so use that whenever you can, unless the question otherwise specifies.}

 

[Born Dancer]

thankyou for everyone's help

 

[FinalFantasy]

yea my fault for putting that "must" word in there. but plz don't get me wrong or take offense, i was just offering an alternative solution for Morning_Glory in light of using alpha and beta and not necessarily the discriminant.

your method is perfectly fine, but i was trying to give as much help as i can to Morning_Glory since she was curious about using alpha and beta to doing the problem ... and like i offered in my explanation to Morning_Glory, using alpha and beta is unnecesarily time-consuming compared to using the discriminant like you did:

hey i didn't take u wrong or take offense or anything
juz saying that she didn't say "must"
im one of those ppl who really dun mind at all, so i won't be offended easily lol ^^

 

[who_loves_maths]

^ lol, okay... i just wanted to clarify my intentions in my last post that's all. it's my fault for putting in the "must" word when she clearly didn't say it was of necessity.
yea so sorry about that

 

[FinalFantasy]

^ lol, okay... i just wanted to clarify my intentions in my last post that's all. it's my fault for putting in the "must" word when she clearly didn't say it was of necessity.
yea so sorry about that

hahaha no need to be sorry. anyway as captain slide suggests.. alternate solutions r cool