SSC CPO SI and ASI 2012 Paper

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Question : 127 of 200

Marks: +1, -0

If ax

^{2}

+ bx + c = a (x – p)

^{2}

, then the relation among a, b, c would be

abc = 1
b $^{2}$ = ac
b $^{2}$ = 4ac
2b = a + c

Solution:

a x^{2}+b x+c=a(x-p)^{2}

⇒ a x^{2}+b x+c

=a x^{2}+a p^{2}-2 a x p

Comparing the corresponding coefficient, b = –2ap and c = ap

^{2}

\ {b}^{2}=4 \ {a}^{2} {p}^{2}

and

\ {c}= {ap}^{2}

and hence,

\ {b}^{2}=4 \ {a}^{2} ×{ {c}}/{ {a}}=4 \ {ac}

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