Question

The equation formed by decreasing each root of

ax² + bx + c = 0 by 1 is 2x² + 8x + 2 = 0, then –

• A. a = – b
• B. b = – c
• C. c = – a
• D. b = a + c

Answer 1

Answer: (B)

b = – c

Answer 2

Let roots of eq. ax² + bx + c = 0

are α, β ⇒ α + β = $\frac{- b}{a}$, αβ = c/a

now roots of 2x² + 8x + 2 = 0 is

α – 1, β – 1

(α – 1) + (β – 1) =$\frac{- 8}{2}$= – 4

– $\frac{b}{a}$ = – 2 $\begin{matrix} b = 2.a \end{matrix}$ $\left\lvert \, \begin{array} { c c c } ( \alpha - 1 ) & ( \beta - 1 ) & = 1 \\ \alpha \beta - ( \alpha + \beta ) & = 0 \\ \mathrm { c } / \mathrm { a } & \mathrm { b } / \mathrm { a } & = 0 \end{array} \right.$

b = - c \end{matrix}$$