Solving a Quadratic Equation by Splitting the Middle Term

Q.

Solve the quadratic equation $x^2-9x+20=0.$

1. 4, 5

2. -5, -1

3. 5, 1

4. -2, 3

Q. If $x=2$ and $x=3$ are roots of the equation $3x^2-2kx+2m=0$, find the value of k and m.
[2 MARKS]

Q. By selling a table for ₹ 24, a trader loses as much percent as the cost price of the table. Calculate the cost price.

1. ₹ 60
2. ₹ 30
3. ₹ 40
4. ₹20

Q. Question 3 (ii)
Find the roots of the following equations:
(ii) $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne -4,7$

Q.

Fill in the blanks to make the statement true: Devangi buys a chair for $₹700$ and sells it for $₹750$.

She earns a profit of _________ $\%$ in the transaction.

Q. Find the roots of the following equations:
(ii) $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne -4,7$

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. Solve $3x^2-8x+4=0$ using factorisation method.

1. Roots: $x=2,x=\frac{2}{3}$
2. Roots: $x=-2,x=\frac{-2}{3}$
3. Roots: $x=3,x=\frac{3}{2}$
4. Roots: $x=-3,x=\frac{-3}{2}$

Q. Match the following to their roots.

1. $x=0,x=-1$
2. $x=-1,x=-2$
3. $x=0,x=-3$
4. $x=-1$

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. -120
3. -20
4. 20

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.

Solve:- 8$x^2$ + 10x +3 = 0

Q.

The expression $x^4+8x^2+16$ can be factorised as

1. $(x^2+x+16{)}^2$

2. $(x^2+x+1{)}^2$

3. $(x^2+4{)}^2$

4. $(x^2+x-4)(x^2-x+4)$

Q.

One leg of a right angled triangle exceeds the other leg by 2 inches. The hypotenuse is 10 inches. Find the length of the shorter leg of the triangle.

1. 4

2. 6

3. 2

4. 8

Q. solve:
$\frac{20\pm \sqrt{400-4\left(5\right)\left(18\right)}}{2\left(5\right)}$=?

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. $1.)a^2-7a+12=0$
$2.)b^2-3b+2=0$ to solve both the equations to find the values of $a$ and $b$ and choose the correct option?

1. $a\ge b$
2. $a<b$
3. $a>b$
4. the relationship between $a$ and $b$ cannot be established.

Q. Solve $4p^2+7=12p$

Q.

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

1. $\pm 1$

2. $3\&2$

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

4. $4\&5$

Q. Solve: $\sqrt{3x^2+1}+\frac{4}{\sqrt{3x^2+1}}=5$

Q. Solve $x^2+6x-7=0$ by the method of completing the square

Q. Match the following to their roots.

1. $x=0,x=-1$
2. $x=-1$
3. $x=0,x=-3$
4. $x=-1,x=-2$

Q. Match the following to their roots.

1. $x=0,x=-1$
2. $x=0,x=-3$
3. $x=-1,x=-2$
4. $x=-1$

Q. Match the following to their roots.

1. $x=-1,x=-2$
2. $x=0,x=-3$
3. $x=0,x=-1$
4. $x=-1$

Q. By selling a table for ₹ 24, a trader loses as much percent as the cost price of the table. Calculate the cost price.

1. ₹ 60
2. ₹ 30
3. ₹ 40
4. ₹20

Q. By selling a table for ₹ 24, a trader loses as much percent as the cost price of the table. Calculate the cost price.

1. ₹ 60
2. ₹ 30
3. ₹ 40
4. ₹20

Q. Solve: $3x^2=2x+8$

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. 14 inches

2. 7 inches

3. 12 inches

4. 20 inches

Q. Solve: ${150x}^2-750x-8=0$

Q.

Factorize $\sqrt{3}$ $x^2$ + 5x + 2$\sqrt{3}$ = 0 into (ax+b)(cx+d)=0. What is the value of a + b + c - d ?