Factorisation

Q. Factorise $x^2+4x+4$.

1. $(x+1)(x+3)$
2. $(x+2)(x+2)$
3. $(x+1)(x+2)$
4. $(x+4)(x+2)$

Q. Find the sum of the roots of the quadratic equation $x^2-7x+12=0.$

1. 7

Q.

The perimeter of a rectangle is 24 cm and its area is 32 sq. cm. Find the length of the longer side.

1. 16 cm

2. 12 cm

3. 4 cm

4. 8 cm

Q.

Find the roots of the quadratic equation $\sqrt{2}$$x^2$ + 7x + 5$\sqrt{2}$ = 0 using factorization method.

1. –5/√2 and –√2

2. 5/√2 and –√2

3. 5/√2 and √2

4. –5/√2 and √2

Q.

A rectangular plot of land is to be enclosed by fencing. One side is along a river and so needs no fence. If the total fencing available is $600m$, find the dimensions of the plot to have maximum area.

Q.

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides (in cm).

1. 2, 5

2. 5, 3

3. 7, 2

4. 12, 5

Q.

Question 6

A wire in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also, find which shape encloses more area?

Q.

Question 5
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Q. Find the roots of the following quadratic equations by the factorization method.
$3\sqrt{2}{x}^2-5x-\sqrt{2}=0$

Q. A motorboat whose speed is $18$ km/h in still water takes $1$ hour more to go $24$ km upstream than to return downstream to the same spot. Find the speed of the stream.
$\left[4\right]$

Q. Factorise $x^2+8x+16$.

1. $(x+8)(x+2)$
2. $(x+2)(x+4)$
3. $(x+4)(x+6)$
4. $(x+4)(x+4)$

Q.

Draw a diagram that shows how the expression can represent the area of a figure. Then simplify the expression.

$(4+1)(x+2x)$

Q. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the altitude of this triangle.

1. $12cm$
2. $14cm$
3. $10cm$
4. $5cm$

Q. Match the quadratic equations with their respective roots.

1. -3 and -2
2. -3 and -5
3. -3 and 2

Q. The perimeter of a rectangle is 24 cm and its area is 32 sq. cm. Find the length of the longer side.

Q. Match the quadratic equations with their respective roots.

1. -3 and -5
2. -3 and -2
3. -3 and 2

Q. $\text{The quadratic equation}{x}^2+7x+12=0\text{can be visualised to be a rectangle}\text{of width}(x+3)\text{and length}$ .

1. ($x+3$)
2. ($x+4$)
3. ($x+1$)
4. ($x+2$)

Q. Find the roots of the following quadratic equations by the factorization method.
$3x^2+5\sqrt{5}x-10=0$

Q.

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides (in cm).

1. 7, 2

2. 5, 3

3. 2, 5

4. 12, 5

Q.

Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$ using factorisation method.

1. $\frac{-5}{\sqrt{2}}$ and – $\sqrt{2}$

2. $\frac{5}{\sqrt{2}}$ and - $\sqrt{2}$

3. $\frac{5}{\sqrt{2}}$ and $\sqrt{2}$

4. $\frac{-5}{\sqrt{2}}$ and $\sqrt{2}$

Q. The roots of the quadratic equation $3x^2+2x-1=0$ are $\frac{1}{3}$ and _____.

1. -1
2. -2
3. 2
4. 1

Q.

Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$ using factorisation method.

1. $\frac{-5}{\sqrt{2}}$ and – $\sqrt{2}$

2. $\frac{5}{\sqrt{2}}$ and - $\sqrt{2}$

3. $\frac{5}{\sqrt{2}}$ and $\sqrt{2}$

4. $\frac{-5}{\sqrt{2}}$ and $\sqrt{2}$

Q. Match the quadratic equations with their respective roots.

1. -3 and -5
2. -3 and -2
3. -3 and 2

Q.

When the square of a number is decreased by 15, it is equal to twice the original number. Find the possible values of the number.

1. 9, 6

2. 5, -3

3. 2, -7

4. 8, 7

Q. Factorize:
$x^2-23x+108$

Q.

Question 5
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Q. ($x^2+4x+3$) can be visualised by the rectangle below. Identify the region depicting the constant term.

1. 
2. 
3. 
4. 

Q.

Factorise the given quadratic equation

$x^2+5x+6=0.$

1. $(x+2)(x+3)$

2. $(x-2)(x-3)$

3. $(x+1)(x+3)$

4. $(x-1)(x-3)$

Q.

Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$ using factorisation method.

1. $\frac{-5}{\sqrt{2}}$ and – $\sqrt{2}$

2. $\frac{-5}{\sqrt{2}}$ and $\sqrt{2}$

3. $\frac{5}{\sqrt{2}}$ and $\sqrt{2}$

4. $\frac{5}{\sqrt{2}}$ and - $\sqrt{2}$

Q.

Find the roots of the quadratic equation $x^2-3x+2=0$, using factorisation method.

1. $1,2$

2. $3,2$

3. $-3,2$

4. $-1,2$