Let a 0. If α is a root of a²x²+bx+c=0, β a root of a²x²-bx-c=0, and 0<α<β, then the root γ of a²x²+2bx+2c=0 satisfies (a) γ= α+β 2 (b) γ=α+ β2 (c) γ=α (d) α<γ<β

Correct answer: (d) α<γ<β Let f(x)=a²x²+2bx+2c. Then f(α)=bα+c and f(β)=3(bβ+c) have opposite signs, so a root γ lies strictly between α and β. JEE Advanced 1989 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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[JEE Advanced 1989] let a 0 if alpha is a root of a 2x 2 bx c

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Let $a\ne0$. If $\alpha$ is a root of $a^2x^2+bx+c=0$, $\beta$ a root of $a^2x^2-bx-c=0$, and $0<\alpha<\beta$, then the root $\gamma$ of $a^2x^2+2bx+2c=0$ satisfies

(a) $\gamma=\frac{\alpha+\beta}2$
(b) $\gamma=\alpha+\frac\beta2$
(c) $\gamma=\alpha$
(d) $\alpha<\gamma<\beta$

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VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (d) $\alpha<\gamma<\beta$

Let $f(x)=a^2x^2+2bx+2c$. Then $f(\alpha)=b\alpha+c$ and $f(\beta)=3(b\beta+c)$ have opposite signs, so a root $\gamma$ lies strictly between $\alpha$ and $\beta$.

JEE Advanced 1989 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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