Solving a Quadratic Equation Using Formula

Q. One of the real roots of the quadratic equation $3x^2-5x-2=0$ is :

1. $-\frac{1}{3}$
2. -3
3. $\frac{1}{3}$
4. 2

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 $\frac{2a+b}{3}$ and $\frac{a+2b}{3}$

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

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

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

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. Arrange the following equations based on the descending order of their root values.(Use quadratic formula )

1. $x^2-6x+9=0$
2. $x^2-2x+1=0$
3. $x^2-4x+4=0$
4. $x^2+2x+1=0$

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

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

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.

Find the roots of the quadratic equation, 3x² – 5x + 2 = 0, using quadratic formula.

1. $\frac{(5\pm 1)}{6}$

2. $\frac{(5\pm 2)}{6}$

3. $\frac{(4\pm 1)}{6}$

4. $\frac{(7\pm 1)}{6}$

Q.

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

1. 650 km/hr

2. 950 km/hr

3. 850 km/hr

4. 750 km/hr