Question

If the roots of the equation a{{x}^{2}}+bx+c=0
are l
and2l
, then [MP PET 1986; MP PET 2002]
A) {{b}^{2}}=9ac B) 2{{b}^{2}}=9ac C) {{b}^{2}}=-4ac D) {{a}^{2}}={{c}^{2}}

Answer 1

Hi ,

It is given that l and 2l are two roots of

the quadratic equation ax² + bx + c = 0 ,

1 ) sum of the roots = - b/a

l + 2l = - b/a

3l = - b/a

l = - b/3a

l² = b² / 9a² ----( 1 )

2 ) product of the roots = c/a

l × 2l = c/a

2l² = c/a

l² = c/2a ---( 2 )

( 1 ) = ( 2 )

b² /9a² = c/2a

2b² = 9ac

Therefore ,

Option ( B ) is correct.

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