Roots of Quadratic Equation by Formula Method

Q.

Find the roots of the quadratic equation by using the quadratic formula the following: $2x^2-3x-5=0$.

Q. If the square of a number is 80 less than 18 times the number, then the number can be .

1. 8 or 10
2. -8 or -10
3. -8 or 10
4. 8 or -10

Q.

If Zeba were younger by $5$ years than what she really is, then the square of her age (in years) would have been $11$ more than five times her actual age. What is her age now?

Q. Using quadratic formula solve the following quadratic equation:

$p^2{x}^2+(p^2-q^2)x-q^2=0,p\ne 0$
[2 Marks]

Q. Using quadratic formula solve the following quadratic equation:

$m^2{x}^2+(m^2-n^2)x-n^2=0,m\ne 0$

1. The roots are : $\frac{2n^2}{m^2},-1$
2. The roots are : $\frac{n^2}{m^2},-6$
3. The roots are : $\frac{n^2}{9m^2},-1$
4. The roots are : $\frac{n^2}{m^2},-1$

Q. Using quadratic formula solve the following quadratic equation:

$m^2{x}^2+(m^2-n^2)x-n^2=0,m\ne 0$

Q. Find the roots of the quadratic equation $a{x}^2+bx+c=0$.

1. $x=\frac{-b\pm \sqrt{b^2-4ac}}{2}$
2. $x=\frac{-b+\sqrt{b^2-4ac}}{4a}$
3. $x=\frac{-b-\sqrt{b^2-4ac}}{4a}$
4. $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Q. If the square of twice a number is 9 more than thrice the square of the given number, then the number can be .

1. 3 or -3
2. 4 or -4
3. 5 or -5
4. 6 or -6

Q.

Solve the following quadratic equation using quadratic formula .

$9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0$

1. The roots are $\frac{5a+b}{3}$ and $\frac{a+2b}{3}$

2. The roots are $\frac{2a+b}{3}$ and $\frac{a-2b}{4}$

3. The roots are $\frac{2a+b}{3}$ and $\frac{a-2b}{3}$

4. The roots are $\frac{2a+b}{3}$ and $\frac{a+2b}{3}$

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.

Using quadratic formula solve the following quadratic equation:

$p^2{x}^2+(p^2-q^2)x-q^2=0,p\ne 0$

1. The roots are : $\frac{q^2}{p^2},-1$

2. The roots are : $\frac{q^2}{p^2},-6$

3. The roots are : $\frac{2q^2}{p^2},-1$

4. The roots are : $\frac{q^2}{9p^2},-1$

Q.

Taylor purchased a rectangular plot of area $634{\text{m}}^2$. The length of the plot is 2 m more than thrice its breadth. The length and breadth respectively is _____ (approximate values).

1. 34.6 m & 11.20 m

2. 88 m & 24 m

3. 32 m & 16 m

4. 44.6 m & 14.20 m

Q.

11 years from now, the age of Peter will be half the square of the age he was 13 years ago. Calculate the current age of Peter.

1. 21 years

2. 7 years

3. 27 years

4. 25 years

Q. If the sides of a right triangle are consecutive natural numbers, then the length of the shortest side is units.

1. 2
2. 3
3. 4
4. 5

Q. Match the following quadratic equations with their corresponding roots.

1. 0 and -8
2. 1 and 3
3. 0 and 6