Question

if (x^2+x+1) is written in the form (x+1/2)^2+q^2 find the possible value of q
pls guys help to do this sum​

Answer 1

Answer:

Step-by-step explanation:

± √3/2  or  ± √(3/4)

Step-by-step explanation:

Since both are same, just written in other forms, we can say

⇒ x² + x + 1 = (x + 1/2)²  + q²

⇒ x² + x + 1 = x² + (1/2)² + 2(x)(1/2) + q²

⇒ x² + x + 1 = x² + 1/4 + x + q²

⇒ 1 = 1/4 + q²

⇒ 1 - 1/4 = q²

⇒ 3/4 = q²

⇒ ± √(3/4) = q   or  ± √3/2 = q

Answer 2

Answer:

Solution :-

Given, p and q be the roots of the equation

x

2

−2x+A=0. So,

p+q=22.....(1)

pq=A...(2)

And, r and s be the roots of the equation

x

2

−18+B=0. So,

r+s=18...(3)

rs=B...(4)

Now, p,q,r and s are in A.P

so let, p=a,q=a+d,r=a+2d,s=a+3d

Now, put these values in equation (1) and (3), we have

a+a+d=2⇒2a+d=2...(5)

And,

a+2a+a+3d=18⇒2a+5d=18...(6)

solving equation (5) and (6),

a=−1, d=4

so p=−1,q=−1+4=3,r=−1+8,s=−1+12=11

Thus,

A=pq=−1×3=−3

B=rs=7×11=77

Then A+B=−3+77=74