Question

(x – 2)(x – 5) = x2 + Bx + C. What are the values of B and C?

Answer 1

Step-by-step explanation:

One of the roots of the equation is b, so just plug it in the equation.

b2+b∗b+c=0

⟹c=−2b2

Another root of the equation is c, so just plug it in the equation.

⟹c2+bc+c=0

⟹c(c+1+b)=0

⟹c=0 or b+c+1=0

⟹c=0 or c=−b−1

⟹−2b2=0 or −2b2=−b−1

⟹b=0 or 2b2−b−1=0

If 2b2−b−1=0

⟹2b2−2b+b−1=0

⟹2b(b−1)+1(b−1)=0

⟹(2b+1)(b−1)=0

⟹(b−1)=0 or 2b+1=0

⟹b=1 or b=−1/2

⟹c=−2(1)2 or c=−2(−1/2)2

⟹c=−2 or c=−1/2

Thus the possible values for (b,c) is (0,0),(1,-2) and (-1/2,-1/2)

Verification is required so, check the three equations namely

1)x2+0(x)+0=0 aka x2=0

both its roots are 0.

2)x2+1(x)−2=0 aka x2+x−2=0

its roots are 1 and -2

and

3)x2+(−1/2)(x)−1/2=0 aka x2−x/2−1/2=0

its roots are -1/2 and 1

Depending on how you interpret the question, the third solution may/may not be valid