help with as question

[wooden briar]

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   +close
   

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[unreal gulch]

bit unsure where to go with this one

rn i've got the bottom equation as a circle formula

but im a bit lost at this point

[lone patrol]

@unreal gulch do you want a hint or the answer

[unreal gulch]

i think i might have got it

are the values between -1/2 and 2

[lone patrol]

Let me check I didnt do that far haha

[unreal gulch]

yh i think its to do with the discriminant right?

i wasnt properly reading that last part which is what i think its trying to say

[lone patrol]

Yeah

It is

👍

[lone patrol]

Yeah intersects so real roots type of thing

[unreal gulch]

yh that makes sense

[lone patrol]

And part B is just the line being a tangent to the circle

[unreal gulch]

so are the values between -1/2 and 2?

[lone patrol]

Yep

[unreal gulch]

ah ty

[lone patrol]

Slope is between and equal to -1/2 and 2

[unreal gulch]

so does that just mean that any lines betwene those gradients is a tangent?

[lone patrol]

No any lines with slope -1/2 and 2 is a tangent

Since they have only one root right

Anything in between intersects the circle and cuts it at 2 points

[unreal gulch]

but does a range of values not imply that anything between the 2 values would satisfy?

i think ive confused myself somewhere tbh

[lone patrol]

Let me show you the figure

[unreal gulch]

ur explanation makes sense its what im thinking as well tbh but it just seems like the question implies otherwise

[lone patrol]

This is the situation basically

Real solution means that when you solve the equations you need a value right

Imagine a quadratic equation ax²+bx+c=0.
This can be written as:
y=ax²+bx+c and y=0

The quad eqn having a real solution implies it has one or two roots right

The two graphs touch or intersect each other

Thats what the question basically asks

What values give roots or what values would cause it to intersect

[unreal gulch]

oh i never thought about it like that

that makes sense

ok yh i understand, then graphically i just draw the y=2x tangent

for part b

ty for the help

[lone patrol]

👍

[unreal gulch]

+close