If the equation $(a - 5) x^{2} + 2 (a - 10) x + a + 10 = 0$ has roots of opposite signs, then

a > 10-

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-15 < a < 5

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-10 < a < 5

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none of these

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Solution

The correct option is D -15 < a < 5
As we are given roots are opposite in sign
So, let us assume $α, - α$ are roots of given equation.
$\Rightarrow$ Sum of roots $= \frac{- b}{a} = 0$
$\Rightarrow \frac{- 2 (a - 10)}{a - 5} = 0$
$\Rightarrow a = 10$
$\Rightarrow (B)$ .

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If the equation (a−5)x2+2(a−10)x+a+10=0 has roots of opposite signs, then

The correct option is D -15 < a < 5As we are given roots are opposite in signSo, let us assume α,−α are roots of given equation.⇒ Sum of roots=−ba=0⇒−2(a−10)a−5=0⇒a=10⇒(B).

If the equation $(a - 5) x^{2} + 2 (a - 10) x + a + 10 = 0$ has roots of opposite signs, then

The correct option is D -15 < a < 5
As we are given roots are opposite in sign
So, let us assume $α, - α$ are roots of given equation.
$\Rightarrow$ Sum of roots $= \frac{- b}{a} = 0$
$\Rightarrow \frac{- 2 (a - 10)}{a - 5} = 0$
$\Rightarrow a = 10$
$\Rightarrow (B)$ .