Solving a Quadratic Equation Using Formula

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 $(1+m^2)x^2+2mcx+c^2-a^2=0$ has equal roots, prove that $c^2=a^2(1+m^2)$.

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

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

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

Q. Solve $2n^2+n+45=0$

Q.

Sum of the first ___ natural numbers is 210.

1. 20

2. 19

3. 21

4. 18

Q.

Question 2 (i)
Find the values of k for each of the following quadratic equations, so that they have two equal roots.
$\left(i\right)2x^2+kx+3=0$

Q.

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

1. 4

2. 3

3. 1

4. 2

Q.

Using quadratic formula find the roots of the quadratic equation $2x^2-7x+3=0$ .

1. $x=\frac{3}{2}$

2. $x=\frac{1}{2}$

3. $x=3$

4. $x=-3$

Q. a) Solve the following equation and give your answer correct to 3 significant figures:
$5x^2-3x-4=0$

b)
Without solving the following quadratic equation, find the value of p for which the roots are equal:
$p{x}^2-4x+3=0$

Q. Find the discriminant of the given equation

1. 2
2. 3
3. 0
4. 1

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 $\frac{2a+b}{3}$ and $\frac{a-2b}{3}$
3. The roots are $\frac{5a+b}{3}$ and $\frac{a+2b}{3}$
4. The roots are $\frac{2a+b}{3}$ and $\frac{a-2b}{4}$

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.
$3\sqrt{2}{x}^2-5x-\sqrt{2}=0$

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

1. $720km/h$
2. $730km/h$
3. $740km/h$
4. $750km/h$

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) $4x^2+4\sqrt{3}x+3=0$

Q. Solve each of the following equation by using the method of completing the square:
$2x^2+5x-3=0$ ?

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:
$x^2-6x+3=0$

Q. Solve the following quadratic equation using quadratic formula. $9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0$

Q. Find the discriminant of the quadratic equation .

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. 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. Find the roots of the following equation using Quadratic formula:
$x-\frac{1}{x}=3,x\ne 0$

Q. An aeroplane leaves an airport and flies due north at a speed of $1000km$ per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of $1200km$ per hour. How far apart will be the two planes after $1\frac{1}{2}$ hours?

Q. Solve the following equation by using the method of completing the square:
$x^2-4x+1=0$

Q. How do you solve $10x^2+9x=499$?

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

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

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)?

1. $3$ kmph
2. $4$ kmph
3. $2$ kmph
4. $5$ kmph