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Quadratic Equations

Short Answer Type

1. Check whether the following are quadratic equations:
(x + 1)² = 2(x – 3)

1383 Views

2. Check whether the following are quadratic equations:
x²– 2x = (–2) (3 – x)

574 Views

3. Check whether the following are quadratic equations:
(x – 2) (x + 1) = (x – 1) (x + 3)

533 Views

4. Check whether the following are quadratic equations:
(x – 3) (2x + 1) = x(x + 5)

542 Views

5. Check whether the following are quadratic equations:
(2x –1) (x–3) = (x + 5)(x–1)

495 Views

6. Check whether the following are quadratic equations:
x² + 3x + 1 = (x – 2)²

186 Views

7. Check whether the following are quadratic equations:
(x + 2)³ = 2x(x² – 1)

156 Views

8. Check whether the following are quadratic equations:
x³ – 4x² – x + 1 = (x – 2)³.

125 Views

Long Answer Type

9. Represent the following problem situations in the form of quadratic equations:
The area of a rectangular plot is 528 m². The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Let breadth of the rectangle = x m Then, length of the rectangle = (2x + 1) m
∵ Area of the rectangle = (2x + 1) x m²
According to the given condition,
(2x + 1)x = 528 ⇒ 2x² + x – 528 = 0
which is a quadratic equation in x.
Solving this equation by factorisation method, we get

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rightwards double arrow

straight x left parenthesis 2 straight x plus 33 right parenthesis minus 16 left parenthesis 2 straight x plus 33 right parenthesis equals 0

rightwards double arrow

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rightwards double arrow

2 straight x plus 33 equals 0 space space or space space straight x space minus space 16 space equals space 0

rightwards double arrow

space space straight x equals fraction numerator negative 33 over denominator 2 end fraction space space or space space straight x space equals space 16

But breadth cannot be -ve.
∴ x = 16
Hence, breadth of the rectangle = 16 m and length of the rectangle = 2 x 16 + 1 = 33 m.

387 Views

Short Answer Type

10. Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

220 Views