Question

If $a{x}^2+bx+c=a(x-p{)}^2$. then the relation among a. b, c would be

• A. abc = 1
• B. $b^2$ = ac
• C. $b^2$ = 4ac
• D. 2b = a+c

Answer 1

The correct option is C $b^2$ = 4ac

$a{x}^2+bx+c=a(x-p{)}^2$
$\Rightarrow a{x}^2+bx+c=a(x^{2}2px+p^2)$
$\Rightarrow a{x}^2+bx+c=a{x}^2-2apx+a{p}^2$
Comparing the corresponding coefficients,
b = -2ap (1)
c = $a{p}^2$
On squaring eq. (1). we get
$\Rightarrow b^2=4a^2{p}^2$
$\Rightarrow p^2=\frac{b^2}{4a^2}$
$\therefore C=a\times \frac{b^2}{4a^2}$ [From eq. (1)]
$\Rightarrow b^2=4ac$