Question

Which of the following are linear :
(i) 3x (x – 2) = 3x^2+ 2x – 7
(ii) (x + 1) (x – 2) = 10
(iii) x (x + 1) = –2x^2+ 7x + 2
(iv) 2x^2 + 7x – 3 = 2x (x + 1)

Answer 1

Heya!!! User ✌

Here's your answer friend,

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==> i) 3x(x - 2) = 3x² + 2x - 7 =0

==> 3x² - 6x = 3x² + 2x - 7 = 0

==> 3x² - 3x² - 6x - 2x - 7 = 0

==> -8x - 7 =0

Here,

the degree of polynomial is 1, hence it is a linear equation.

ii) (x + 1)(x - 2) = 10

==> x² - 2x + x - 2 = 10

==> x² -x - 2 = 10

==> x² -x -12 = 0

Here, the degree of polynomial is 2, Hence it is not linear equation, it is a quadratic equation.

iii) x(x + 1) = -2x² + 7x + 2

==> x² + x = -2x² + 7x + 2

==> x² + 2x² + x - 7x - 2

==> 3x² - 6x - 2

Here, degree of the polynomial is 2,
Hence, it is not a linear equation, but it is a quadratic equation.

iv) 2x² + 7x - 3 = 2x (x + 1)

==> 2x² + 7x - 3 = 2x² + 2x

==> 2x² - 2x² + 7x - 2x -3

==> 5x - 3

Here, the degree of the polynomial is 1,
Hence, it is a linear equation.

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