Solving Second Degree Equations

Q.

During a practice match, a softball pitcher throws a ball whose height at any instant from ground level is given by the equation h = $-16t^2$ + 24t + 1 , where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet from the ground level?

1. 2.2 secs, 3.8 secs

2. 5.4 secs, 6.2 secs

3. 0.25 secs, 1.25 secs

4. 7 secs, 5 secs

Q.

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h=-16t^2+24t+1$, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

1. 2.2 and 3.8 secs

2. 5.4 and 6.2 secs

3. 0.25 and 1.25 secs

4. 7 and 5 secs

Q.

During a practice match, a softball pitcher throws a ball, whose height can be modeled by the equation $h=-16t^2+24t+1$, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

1. 2.2, 3.8 secs
2. 5.4, 6.2 secs
3. 0.25, 1.25 secs
4. 7, 5 secs

Q. Using the factorisation method, find the roots of the following quadratic equation: $x^2-10x+24=0$

Q. The roots of the quadratic equation $2x^2-5x+3=0$ are .

1. 1 and 6
2. 1 and $\frac{3}{2}$
3. 1 and $\frac{2}{3}$

Q. Solve the following quadratic equation:
$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne 4,7$

Q.

During a practice match, a softball pitcher throws a ball whose height can be modeled by the equation $h=-16t^2+24t+1$, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

1. 2.2 and 3.8 secs

2. 5.4 and 6.2 secs

3. 0.25 and 1.25 secs

4. 7 and 5 secs

Q. Solve the following quadratic equation by factorization, the roots are :
$9x^2$ - 3x - 2 = 0

1. $\frac{2}{5},-\frac{1}{3}$
2. $\frac{1}{3},-\frac{1}{3}$
3. $\frac{2}{3},-\frac{1}{6}$
4. $\frac{2}{3},-\frac{1}{3}$

Q. The multiplicative inverse of $-1\times \frac{-2}{5}$ is $\frac{p}{2}$, $p$ is

Q. Using the factorisation method, find the roots of the following quadratic equation:
$\frac{x}{x-1}+\frac{x-1}{x}=\frac{5}{2}$

Q. Solve the given quadratic equation by factorization method
$\frac{4}{x}-3=\frac{5}{2x+3}x\ne 0,\frac{-3}{2}$

Q. Solve the following quadratic equation by factorization method.$\frac{1}{a+b+x}+\frac{1}{a}+\frac{1}{b}+\frac{1}{x}=0$$,a+b\ne 0$

Q. When $\frac{1}{3}$ is divided by the reciprocal of a particular number, the result is $8$ less than the number. Find the number.

1. $8$
2. $12$
3. $3$
4. $6$

Q. $\text{If one of the zeros of quadratic polynomial}(k-1)x^2+kx+1\text{is}-3,$
$\text{then find the value of}k.$

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

Q.

If the length of the square is reduced by $2m$, then the area becomes $49m^2$. Find the length of the original square.

1. $7m$

2. $4m$

3. $-5m$

4. $9m$

Q. Solve the following quadratic equations by factorization method:
$x+\frac{1}{x}=\frac{26}{5}$

1. $\{5,\frac{1}{5}\}$
2. $\{-5,\frac{1}{5}\}$
3. $\{5,\frac{-1}{5}\}$
4. None of these

Q. If the root of the equation $x^2+a^2=8x+6a$ are real, then find the interval $a$ belongs to.

1. $a\in [-2,8]$
2. $a\in [2,8]$
3. $a\in (-2,8)$
4. $a\in (2,8)$

Q. The roots of the quadratic equation $x^2-5x+6=0$ are .

1. 1 and 6
2. 2 and 3
3. -2 and -3
4. -1 and -6

Q.

If $\alpha$ and $\beta$ are the zeros of a polynomial
$f\left(x\right)=6x^2+x-2$, find the values of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$.

1. $-\frac{25}{12}$

2. $\frac{25}{12}$

3. $\frac{25}{36}$

4. $\frac{12}{25}$

Q. Positive root of the equation ${\left(\frac{3x-1}{2x+3}\right)}^2-5\left(\frac{3x-1}{2x+3}\right)+4=0$ is _____.

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

Q.

If one root of the equation $2x^2+ax+6=0$ is $3$, then find the value of $a$

1. -8

2. 7

3. 3

4. -5

Q. Solve the following quadratic equation.
$\surd 3x^2+10x+7\surd 3=0$

Q. Solve the following quadratic equation.
$x^2+6x+5=0$

Q. State whether true or false:

1. true
2. false

Q. Knowing that 2 and 3 are the roots of the equation $2x^3+m{x}^2-13x+n=0,$ determine m+n+2(p)?where p is the third root of the given equation.

Q. Solve the following quadratic equation.
$\surd 3x^2-2\surd 2x-2\surd 3=0$

Q. If a and b are the roots of the equation $x^2-1=0$ the form of quadratic equation whose roots are 2a and 2b will be-

1. $x^2-4\sqrt{2}=0$
2. $x^2+4=0$
3. $x^2-4=0$
4. $x^2+4\sqrt{2}=0$

Q. Find the nature of the roots of the following quadratic equation:
$5x^2-4x+1=0$

Q. Solve the following quadratic equation.
$x^2-(\sqrt{3}+1)x+\sqrt{3}=0$

Q. Solve the following quadratic equation.
$3\surd 7x^2+4x+\surd 7=0$