quadratics basic

given a quadratic equation f(x)=ax2+bx+c

what are the conditions for

1}both roots to be greater than a specified number k

2}given number k lies between both the roots

3}both roots are confined within numbers p and q

it would be very good if u r able to explain graphically. this does not mean non grpahical solutions are not allowed{hehehe}

11 Answers

39
Dr.House ·

subash it would be fine if u would post the graphs here.

3
msp ·

1
Philip Calvert ·

yes they are correct but what abt the last one.....ok even that seems correct ..
not much probs here...

3
msp ·

hey guys does my graph gives any sense to the question.pls comment.

21
tapanmast Vora ·

part 3)

the fol. are two conditions.....
1. f(p) * f(q) > 0
2. f'(p) * f'(q) < 0

one more :
let x1 be such that f'(x1) = 0;
then f(p) * f(x1) < 0

obviously (b2 - 4ac > 0 )

these 3 inequations shall defiitley clinch it!!! [1]

11
rkrish ·

1)

11
rkrish ·

2)

11
rkrish ·

3)

p < -b/2a & q > -b/2a and af(p) > 0 & af(q) > 0

3
iitimcomin ·

3
iitimcomin ·

SORRY FOR POOR DIAGRAMS!!!!!

21
tapanmast Vora ·

mathie is my soln correct?

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