Question

Two candidates attempts to solve a quadratic equation of form \(x^2+px+q=0\) One starts with a wrong value of p and find the roots to be 2 and 6 the other starts with a wrong value of q and finds the roots to be 2, -9 the correct roots are :

Answer 1

Just put in the roots into the quadratic equations, you will get 4 equations in two variables, solve them to get the value of correct p and q. And then solve the quadratic equation to get the right roots.

Answer 2

Ok i'll try that

Answer 3

By using the relation between roots and coefficient,
-p=(2+6)
p=-8
q=(2)(-9)
= -18
x2-8x-18=0
solve this equation.
(x+10)(x-2)=0
x=-10 or 2

Answer 4

Oh Nice!

Answer 5

But they start with wrong value of p

Answer 6

I was thinking 'One starts with a wrong value of p and find the roots to be 2 and 6', that means q is correct, that is q =2x6 =12
' the other starts with a wrong value of q and finds the roots to be 2, -9' that means p is correct
-p = -9+2
p =7
just put the values into the equation and solve it..
Dunno if it is correct..

Answer 7

Yeah that's right :) @Callisto

Answer 8

-3 and -4 ?

Answer 9

That's what i've got.. :S

Answer 10

ok thats right :D
Thanks everyone :)

Answer 11

I think Vieta's formulas would work in here

Answer 12

What's Vieta's formula ?

Answer 13

http://en.wikipedia.org/wiki/Vieta%27s_formulas