Welcome to your ACT 1 Alg: Solve quadratics equations

$Q_{1}:$ For what values of $x$ is $x^{2} − 3x − 10 = 0$?

$Q_{2}:$ If $3x^{2}-\frac{1}{2}x=0$ and $x > 0$, what is the value of $x$?

$Q_{3}:$ How many roots larger than $5$ does $x^{2} − 3x + 2$ have?

$Q_{4}:$ Solve $6x^{2}-2x− 7$

$Q_{5}:$ Solve $x^{2}-18$

$Q_{6}:$ Factor $3x^{2}+4x+1$.

$Q_{7}:$ Given $f(x)=-(x+2)(x-4)$ , find the $x$-intercepts.

$Q_{8}:$ Which of the following is an equivalent form of the equation of the graph shown

$Q_{9}:$Which of the following is solution of $3x^2-48=-21$

$Q_{10}:$ If r and s are two solutions of the equation $x^{2}-3x=28$, which of the following is the value of $r+s$?

$Q_{11}:$ Solve $2x^{2}-6x-7=0$

$Q_{12}:$ 1 If $x^{2}-10 x=75$ and $x < 0$ , what is the value of $x + 5$ ?

$Q_{13}:$ In the quadratic equation $x^{2}-rx=\frac{k^{2}}{4}$, $k$ and $r$ are are constants. What are the solutions for $x $?

$Q_{14}:$ Which of the following equations has no real solution?

$Q_{15}:$ For which of the following quadratic equations is the sum of its roots equal to the product of its roots?

$Q_{16}:$ What is the greatest integer k for which the equation $x^{2} + 5x + k = 0$ has real solutions?

$Q_{17}:$ The product of the roots of a quadratic equation is $−15$ and their sum is $−2$. Which of the following could be the quadratic equation?

$Q_{18}:$ If the sum of two numbers is equal to 17 and their product is equal to 60, what are the numbers?

$Q_{19}:$ If the area of a rectangle is 46 square units and its longest side is 12 units longer than its shortest side, what are the lengths of the sides?

$Q_{20}:$ The difference between the squares of two consecutive odd numbers is equal to 40. Find both numbers.

$Q_{21}:$ Find two numbers such that their sum equals $15$ and their product equals $36$

$Q_{22}:$Which of the following is solution of $x^2+2x=-2$

$Q_{23}:$ Jon jumped off a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function $h(s) = -16s^{2} + 16s + 480 $, where $s$ is the time in seconds and $h$ is the height in feet. Jon hit the water after how many seconds?

$Q_{24}:$ If a toy rocket is launched vertically upward from ground level with an initial velocity of $128$ feet per second, then its height $h$ after $t$ seconds is given by the equations $h(t) = -16t^{2} + 128t$ (if air resistance is neglected). How long will it take for the rocket to return to the ground?

$Q_{25}:$ Find the value of $k$ for which the quadratic equation $2x^{2}-kx+1=0$ has equal roots.