If x2-3 x-5-0 and a x2-b x-c-0 have a root in common and a- b- c - N- then minimum value of a-b-c-

The correct option is C 9 Roots of x^2 + 3x + 5 = 0 are complex. ∴ a/1=b/3=c/5=λ ⇒ a = 3 λ b = 3 λ c = 5 λ ⇒ a+b+c= 9 λ ∴ Min value of a + b + c = 9 ...

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Byju's Answer

Standard XII

Mathematics

Common Roots

If x2+3 x+5=0...

Question

If $x^{2} + 3 x + 5 = 0$ and $a x^{2} + b x + c = 0$ have a root in common and a, b, c $ϵ$ N, then minimum value of a + b + c =

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Solution

The correct option is C
9

Roots of $x^{2} + 3 x + 5 = 0$ are complex.
$∴ \frac{a}{1} = \frac{b}{3} = \frac{c}{5} = λ \Rightarrow \begin{matrix} a = 3 λ b = 3 λ c = 5 λ \end{matrix} \Rightarrow a + b + c = 9 λ$
$∴$ Min value of a + b + c = 9

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If x2+3x+5=0 and ax2+bx+c=0 have a root in common and a, b, c ϵ N, then minimum value of a + b + c =

The correct option is C 9 Roots of x2+3x+5=0 are complex. ∴ a1=b3=c5=λ⇒ a=3λb=3λc=5λ⇒a+b+c=9λ ∴ Min value of a + b + c = 9

If $x^{2} + 3 x + 5 = 0$ and $a x^{2} + b x + c = 0$ have a root in common and a, b, c $ϵ$ N, then minimum value of a + b + c =

The correct option is C
9

Roots of $x^{2} + 3 x + 5 = 0$ are complex.
$∴ \frac{a}{1} = \frac{b}{3} = \frac{c}{5} = λ \Rightarrow \begin{matrix} a = 3 λ b = 3 λ c = 5 λ \end{matrix} \Rightarrow a + b + c = 9 λ$
$∴$ Min value of a + b + c = 9