Question

Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Answer 1

Let αα and ββ be the roots of the quadratic equation x2+px+q=0x2+px+q=0 Given that, A starts with a wrong value of p and obtains the roots as 2 and 6. But this time q is correct. i.e., a product of roots =q=α.β=6×12=12=q=α.β=6×12=12 ...(i) and B starts with a wrong value of q and gets the roots as 2 and -9. But this time p is correct. i.e., the sum of roots ._ =p=α+β=−9+2=−7=p=α+β=−9+2=−7 ...(ii) (α−β)2=(α+β)2−4αβ(α−β)2=(α+β)2−4αβ (−7)2−4.12=49−48=1(−7)2−4.12=49−48=1 [from Eqs. (i) and (ii)] α−β=1α−β=1 Now, from Eqs. (ii) and (iii), we get α=−3 and β=−4α=−3 and β=−4 which are correct roots.