Question

The discriminant of the equation (2a + b) x = x2 + 2ab is a. (2a + b2) b. (2a – b)2 c. (2a + b)2 d. (2a –b2)

Answer 1

Step-by-step explanation:

Find the attachment for the solution

Answer 2

Answer:

Required discriminant is (2a-b)²

So, option b is the correct option.

Step-by-step explanation:

Given equation is

$(2a + b)x = {x}^{2} + 2ab \\ {x}^{2} - (2a + b)x + 2ab = 0 .....(1)$

We want to find discriminant of the given quadratic equation.

We know, discriminant of

$p {x}^{2} + qx + r = 0 \: is \: {q}^{2} - 4pr$

For example,

We are taking a quadratic equation

${x}^{2} + 2x + 1 = 0....(2)$

We are comparing the equation with

$p {x}^{2} + qx + r= 0$

and get

$p = 1 \\ q= 2 \\ r= 1$

So, discriminant of equation (2) is

${2}^{2} - 4 \times 2 \times 1 = 4 - 8 = - 4$

Now,we are comparing equation (1) with

$p {x}^{2} + qx + r = 0$

and get

$p = 1 \\ q = - (2a + b) \\ r = 2ab$

So, required discriminant of given quadratic equation

${q}^{2} - 4pr \\ = { ( - (2a + b))}^{2} - 4 \times 1 \times 2ab \\ = {(2a + b)}^{2} - 8ab \\ = {(2a)}^{2} + 2 \times 2a \times b + {b}^{2} - 8ab \\ = {(2a)}^{2} - 4ab + {b}^{2} \\ = {(2a - b)}^{2}$

Equation related two more questions:

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