Solving by Factorization method

Q.

Find the roots of the quadratic equation $6x^2-x-2=0$.

Q.

In a class test, the sum of Shefali’s marks in Mathematics and English is $30$. Had she got $2$ marks more in Mathematics and $3$ marks less in English, the product of their marks would have been $210$. Find her marks in the two subjects.

Q.

Solve the following quadratic equation by factorisation method.

$3x^2-x-10=0$

Q. Solve for the roots of the quadratic equation $x^2-5x+6=0$

1. 5, 1
2. 2, 3
3. -5, -1
4. -2, 3

Q.

Factorize $\sqrt{3}$ $x^2$ + 5x + 2$\sqrt{3}$ = 0 by splitting the middle term and find the value of x.

1. $x=\frac{-2}{\sqrt{3}},x=-\sqrt{3}$

2. $x=\frac{\sqrt{2}}{\sqrt{3}},x=-\sqrt{2}$

3. $x=\frac{2}{\sqrt{3}},x=\sqrt{3}$

4. $x=\frac{-3}{\sqrt{2}},x=\sqrt{3}$

Q. By selling an item for ₹24, the shopkeeper earns the percent profit equal to cost price of the item. Find the cost price of the item.

1. -120
2. -20
3. 120
4. 20

Q.

Factorise the given quadratic equation

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

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

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

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

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

Q. If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is :

1. 30 km/hr
2. 70 km/hr
3. 35 km/hr
4. 60 km/hr

Q.

Solve for x : $3(81{)}^x+3=9^{x+1}+9^x$.

1. $\pm 1$

2. $\pm \frac{1}{2}$

3. $3\&2$

4. $4\&5$

Q. The product of a number and the one obtained by decreasing it by 7 is -12. Then, the possible values for the number are .

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

Q. Which of the following satisfies the equation $a^2{b}^2{x}^2-b^{2}x-a^{2}x+1=0?$

1. $-\frac{1}{b^2}$
2. $\frac{1}{b^2}$
3. $\pm \frac{1}{b^2}$
4. $-\frac{1}{a^2}$