a) Given that. x2+2x+1=(4−x)2+3
⇒x2+2x+1=16+x2−8x+3
⇒10x−18=0
Which is not of the form ax2 + bx + c a ≠ 0. Thus the equation is not a quadratic equation.
b) Given that. −2x2=(5−x)(2x−25)
⇒−2x2=10x−2x2−2+2x5
⇒50x+2x−10=0
⇒52x−10=0
Which is also not a quadratic equation
c) Given that. (k+1)x2+32 x=7, where k−=−1
k=−1
⇒x2(−1+1)32+x=7
⇒3x−14=0
Which is also not a quadratic equation.
d) Given that. x3−x2=(x−1)3
x3−x2=x3−3x2(1)+3x(1)2−(1)3
[∴(a−b)3=a3−b3+3ab2−3a2b]
x3+3x2−3x+1=0
2x2−3x+1=0
Which represents a quadratic equation because it has the quadratic form
ax2+bx+c=a≠0