# Solving a Quadratic Equation Using Formula

## Trending Questions

**Q.**

The number of the real roots of the equation ${\left(x+1\right)}^{2}+\left|x-5\right|=\frac{27}{4}$ is

**Q.**If the quadratic equation (1+m2)x2+2mcx+c2−a2=0 has equal roots, prove that c2=a2(1+m2).

**Q.**

Solve the following quadratic equation using quadratic formula .

9x2−9(a+b)x+(2a2+5ab+2b2)=0

The roots are 2a+b3 and a+2b3

The roots are 2a+b3 and a−2b3

The roots are 5a+b3 and a+2b3

The roots are 2a+b3 and a−2b4

**Q.**Solve 2n2+n+45=0

**Q.**

Sum of the first

20

19

21

18

**Q.**

**Question 2 (i)**

Find the values of k for each of the following quadratic equations, so that they have two equal roots.

(i)2x2+kx+3=0

**Q.**

If from a positive number, twice its reciprocal is subtracted, we get 1. Then the number is ___.

4

3

1

2

**Q.**

Using quadratic formula find the roots of the quadratic equation 2x2−7x+3=0 .

x=32

x=12

x=3

x=−3

**Q.**a) Solve the following equation and give your answer correct to 3 significant figures:

5x2−3x−4=0

b)

Without solving the following quadratic equation, find the value of p for which the roots are equal:

px2−4x+3=0

**Q.**Find the discriminant of the given equation

- 2
- 3
- 0
- 1

**Q.**Solve the following quadratic equation using quadratic formula. 9x2−9(a+b)x+(2a2+5ab+2b2)=0

- The roots are 2a+b3 and a+2b3
- The roots are 2a+b3 and a−2b3
- The roots are 5a+b3 and a+2b3
- The roots are 2a+b3 and a−2b4

**Q.**Sum of the squares of two consecutive positive even integers is 100; find those numbers by using quadratic equations.

**Q.**Find the roots of the following quadratic equations by the factorization method.

3√2x2−5x−√2=0

**Q.**A plane left 30 minutes later then the scheduled time and in order to reach the destination 1500 km away in time, it had to increase the speed by 250 km/h from the usual speed. Find its usual speed.

- 720 km/h
- 730 km/h
- 740 km/h
- 750 km/h

**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.

**Q.**

**Question 2 (iii)**

Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

(iii) 4x2+4√3x+3=0

**Q.**Solve each of the following equation by using the method of completing the square:

2x2+5x−3=0 ?

**Q.**What is a "Discriminant"?

**Q.**A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

**Q.**Solve the following equation by using the method of completing the square:

x2−6x+3=0

**Q.**Solve the following quadratic equation using quadratic formula. 9x2−9(a+b)x+(2a2+5ab+2b2)=0

**Q.**Find the discriminant of the quadratic equation $3\sqrt{3}{x}^{2}+10x+\sqrt{3}=0$.

**Q.**Find the roots of the quadratic equation ax2+bx+c=0.

- x=−b±√b2−4ac2
- x=−b−√b2−4ac4a
- x=−b+√b2−4ac4a
- x=−b±√b2−4ac2a

**Q.**One of the real roots of the quadratic equation 3x2−5x−2=0 is :

- −13
- -3
- 13
- 2

**Q.**Find the roots of the following equation using Quadratic formula:

x−1x=3, x≠0

**Q.**An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 112 hours?

**Q.**Solve the following equation by using the method of completing the square:

x2−4x+1=0

**Q.**How do you solve 10x2+9x=499?

**Q.**Using quadratic formula solve the following quadratic equation: [3 MARKS]

9x2−9(a+b)x+(2a2+5ab+2b2)=0

**Q.**John is faster than Jude. John and Jude each walk 20 km. The sum of their speeds is 9 km/hr and the sum of their time taken is 9 hrs. What is the speed of Jude (in kmph)?

- 3 kmph
- 4 kmph
- 2 kmph
- 5 kmph