Solving by Factorization Method

Q.

By increasing the list price of a book by ₹10, a person can buy 10 books less for ₹1200. The original price of the book was :

1. ₹40
2. ₹100
3. ₹24
4. ₹30

Q.

The difference of the square of a number and $8$ is equal to $7$ times that number. Find the positive solution.

Q.

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

1. $1,2$

2. $-1,2$

3. $3,2$

4. $-3,2$

Q.

In a right-angled triangle, the length of its base is one less than twice the perpendicular, and the hypotenuse is one more than twice the perpendicular. Find the length of the base, perpendicular and hypotenuse if the perimeter is$40\mathrm{cm}$.

Q.

One leg of a right angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

1. 12 inches

2. 7 inches

3. 20 inches

4. 14 inches

Q. What is the next step to find all the roots of a quadratic equation which has been factorized?

1. Equate both factors to 1
2. Equate the first factor to 0
3. None of the above
4. Equate both factors to 0

Q. Nikhil expressed the quadratic equation $x^2+10x+16=0$ in the form $x^2+px+qx+16=0$ such that the product of p and q is 16. Choose the correct values of p and q.

1. p = 1, q = 16
2. p = -2, q= -8
3. p = 2, q = 8
4. p = 2, q = 5

Q.

How do you factor $x^4-y^4$?

Q.

How do you solve $a^2+11a=-18$?

Q.

$A$ and $B$ together can do a piece of work in $24$ days. $B$ takes $20$ days more than $A$ for doing the same work alone. In how many days $A$ and $B$ alone can do the same work?

Q.

Solve the following quadratic equation: $x^2=15$

1. x= √15

2. x= - √15

3. x = √15 or x = - √15

4. x = ± 15

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 - $\sqrt{2}$