The general form of any quadratic equation is
ax2 + bx + c = 0
Here a ≠ 0
If the expression can be expressed in the general form, we may say that the given expression is quadratic equation.
Question :
(i) (x + 1)² = 2 (x – 3)
Solution :
(x + 1)² = 2 (x – 3) can be rewritten as
(a + b)² = a2 + 2ab + b2
x²+ 2 x + 1 = 2 x – 6
x²+ 2 x – 2 x + 1 + 6 = 0
x² + 7 = 0
This exactly matches the general form of quadratic equation. So, the given equation is quadratic equation.
(ii) x² – 2 x = (-2) (3 – x)
Solution :
x² – 2 x = - 6 + 2 x
x² – 2 x – 2 x + 6 = 0
x² – 4 x + 6 = 0
This exactly matches the general form of quadratic equation.
(iii) (x - 2) (x + 1) = (x - 1) (x + 3)
Solution :
x² + 1x – 2x - 2 = x² + 3x - 1x - 3
x² - 1x - 2 = x² + 2x - 3
x² - x²- 1x - 2x - 2 + 3 = 0
- 3x + 1 = 0
It does not match with the general form of quadratic equation. So the given equation is not a quadratic equation.
(iv) (x - 3) (2x + 1) = x (x + 5)
Solution :
2x² + 1x – 6x - 3 = x² + 5x
2x² – 5x - 3 = x² + 5x
2x²- x² - 5x – 5x - 3 = 0
x² - 10x - 3 = 0
This exactly matches the general form of quadratic equation. So the given equation is a quadratic equation.
(v) (2 x - 1) (x - 3) = (x + 5) (x - 1)
Solution :
2 x² - 6 x – x + 3 = x² - 1 x - 5 x - 5
2 x² - 7 x + 3 = x² - 6 x - 5
2 x²- x²- 7 x + 6 x + 3 + 5 = 0
x² - 1 x + 8 = 0
This exactly matches the general form of quadratic equation. So, the given equation is a quadratic equation.
(vi) x² + 3 x + 1 = (x - 2)²
Solution :
x² + 3 x + 1 = x² - 2 x (2) + 2²
x² + 3 x + 1 = x² - 4 x + 4
x²- x² + 3 x + 4 x + 1 - 4 = 0
7 x - 3 = 0
This does not match the general form of quadratic equation. So, the given equation is not a quadratic equation.
(vii) (x + 2)³ = 2 x (x² - 1)
Solution :
x³ + 3 (x²) (2) + 3 (x) (2)² + 2³ = 2 x³ - 2 x
x³ + 6 x² + 12 x + 8 = 2 x³ - 2 x
x³ - 2 x³ + 6 x² + 12 x + 2 x + 8 = 0
- x³ + 6 x² + 12 x + 2 x + 8 = 0
This does not exactly match the general form of quadratic equation. So the given equation is not a quadratic equation.
(vii) x³ - 4 x² - x + 1 = (x - 2)³
Solution :
x³ - 4 x² - x + 1 = x³ - 3 (x²) (2) + 3 (x) (2)² - 2³
x³ - 4 x² - x + 1 = x³ - 6 x² + 12 x - 8
x³- x³ - 4 x² + 6 x² - x - 12 x + 1 + 9 = 0
2 x² - 13 x + 10 = 0
This exactly matches with the general form of quadratic equation. So the given equation is a quadratic equation.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Jul 02, 25 07:06 AM
Jul 01, 25 10:27 AM
Jul 01, 25 07:31 AM