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2x^2+ax+8=0 , find possible values for a ?

2x^2+ax+8=0 , find possible values for a ? I'm struggling to visualize the data.

Try completing the square to get something in the form

2(x+b)^2+c

Reply 2

Zacken

Original post by nafisaR

2x^2+ax+8=0 , find possible values for a ? I'm struggling to visualize the data.

Uh, under what conditions...? If you don't impose any conditions, then

a

can be anything...

Reply 3

gdunne42

Original post by nafisaR

2x^2+ax+8=0 , find possible values for a ? I'm struggling to visualize the data.

Assuming that the question states that there are one or more real solutions, or you can assume that's what they mean because of the maths you have been studying, then you could use the discriminant.

Posted from TSR Mobile

(edited 7 years ago)

Reply 4

RogerOxon

Original post by Zacken

Uh, under what conditions...? If you don't impose any conditions, then

a

can be anything...

You basically have a curve of

y=2X^2

, with a translation on both axes. To have at least one real solution, you need it to touch / cross the x axis.

To visualise what you have, draw

y=2X^2

, then

y=2X^2+c

and, finally,

y=2(x+b)^2+c

.

What is the minimum value of

y

for the equation

y=2X^2+c

? For the curve to touch / dip below the x axis, what condition must be satisfied?

Reply 5

Notnek

Original post by RogerOxon

You basically have a curve of

y=2X^2

, with a translation on both axes. To have at least one real solution, you need it to touch / cross the x axis.

To visualise what you have, draw

y=2X^2

, then

y=2X^2+c

and, finally,

y=2(x+b)^2+c

.

What is the minimum value of

y

for the equation

y=2X^2+c

? For the curve to touch / dip below the x axis, what condition must be satisfied?

Is this in reply to the OP's comment : "I'm struggling to visualize the data."?

It should be said though that using the discriminant here is the standard/quickest approach for this question.

And did you intend to quote @Zacken ? His comment was related to the fact that the OP hadn't given the whole question e.g. the question should have said that the quadratic has real roots (I'm guessing this was the actual question).

Reply 6

RogerOxon

Original post by notnek

Is this in reply to the OP's comment : "I'm struggling to visualize the data."?

Yes,

Original post by notnek

It should be said though that using the discriminant here is the standard/quickest approach for this question.

Yes, but it is important to understand what this represents on the graph.

Original post by notnek

And did you intend to quote @Zacken ? His comment was related to the fact that the OP hadn't given the whole question e.g. the question should have said that the quadratic has real roots (I'm guessing this was the actual question).