﻿ If b > a, then the equation (x – a) (x – b) – 1 = 0, has : Kaysons Education

# If b > a, Then The Equation (x – a) (x – b) – 1 = 0, Has

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## Question

### Solution

Correct option is

One root in (– a) and other in (b, + )

y = x2 – x (a + b) + ab – 1

Above equation represents a parabola with vertex

At x = a, x = b both y = – 1 where a < b.

If has roots of the equation y = f (x) be α and β, then f (α) = 0, f (β) = 0

From the figure α < a and β > b

Hence one root is in (– ∞, a) and the other is in (b, + ∞).

#### SIMILAR QUESTIONS

Q1

If the roots of the equation x2 + px – q = 0 are tan 300 and tan 150, then the value of 2 + q – p is

Q2

If α, β, γ are the roots of the equation x3 + ax + b = 0, then

Q3

Let α, β be the roots of x2 – x + p = 0 and γ, δ be the roots of x2 – 4x + = 0. If α, β, γ, δ are in G.P., then the integral values of p and qrespectively, are

Q4

Let P, Q, R be defined as

P = a2b + ab2 – a2c – ac2,

Q = b2c + bc2 – a2b – ac2

R = a2c + c2a – c2b – cb2

Where abc are all + ive and the equation Px2 + Qx + R = 0 has equal roots then abc are in

Q5

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Q10

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