Question

One of the two students, while solving a quadratic equation in x, copied the constant term incorrect and got the roots 3 and 2. The other copied the constant term and coefficient of r correctly and got his roots as -6 and I respectively. The correct roots are​

Answer 1

Answer:

i was bored in class one day and wondered to myself if there were any quadratics x2+ax+b such that a and b are the zeros. I found two: x2+x−2, and x2−12x−12. The comments suggested x2+0x+0, though this seems trivial. I wonder if this applies to other degree polynomials. Clearly it never works for a linear, except for x+0=0, as if x+a=0, x=−a, not a. What about cubics, quadratics, or even higher powers? In general, xn works..

Hope it is helpful to you

Answer 2

Answer:

Let the correct equation be x

2

+ax−6,

Let the in correct equation be x

2

+ax+b,

b=product of roots=2×3=6,

a=−sum of roots=−(2+3)=−5,

Therefore the correct equation is given by

x

2

−5x−6=0

x

2

−6x+x−6=0

(x−6)(x+1)=0,

x=−1,6