Question

given that 1/2 and -3 are the roots of the equation 0=ax^ 2 + bx + c , find a,b,c, where a,b and c are the least possible integers​

Answer 1

Answer:

Step-by-step explanation:

Since roots are two consecutive integers, let us assume n and n+1 are the roots.

Now,

2n+1=b

And n(n+1)=c

For real values,

b2  −4c≥0

Now,  

b  2  −4c

=(2n+1)  2  −4(n)(n+1)

=4n  2  +4n+1−4n  2  −4n =1

Hence, assertion is correct.  

Considering the reason,

B 2 −4AC

=(b2−4ac)2 +16(ab2 c)

=b2 −8ab2 c+16ac2 +16ab2 c

=b2 +8ab2 c+16ac2

 

=(b2 +4ac)2

 

Thus, the discriminant is perfect square.

This yields real roots.

However, it is not the correct explanation of Assertion.