Question 1 :
Find the roots of the following quadratic equation by using the quadratic formula <br>$4{x^2} + 3x + 5 = 0$<br>
Question 2 :
The difference of two natural numbers is $4$ and the difference of their reciprocals is $\dfrac{1}{3}$. Find the numbers.
Question 3 : The following <span>equation </span>is a quadratic equation.<div> $(x \, + \, 2)^3 \, = \, x^3 \, - \, 4$</div>
Question 6 :
Determine whether the equation <span>$\displaystyle 5{ x }^{ 2 }=5x$ is quadratic or not.</span>
Question 7 : <div>The following equation is a qudratic equation.</div><div> $16x^2 \, - \, 3 \, = \, (2x \, + \, 5)(5x \, - \, 3)$</div>
Question 8 :
Squaring the product of $z$ and $5$ gives the same result as squaring the sum of $z$ and $5$. Which of the following equations could be used to find all possible values of $z$?
Question 9 :
The number of solutions of the equation,$2\left\{ x \right\} ^{ 2 }+5\left\{ x \right\} -3=0$ is
Question 11 :
The product of two consecutive integers is $600$. Find the second integer.<br/>
Question 12 :
Which of the following equations has $2$ as one of the roots?<br/>
Question 14 :
If the roots of the quadratic equation $x^2+px+q=0$ are $tan\:15^{\circ }$ and $tan\:30^{\circ }$ respectively, then the value of $2+q-p$ is :<br><br>
Question 15 :
If the quadratic equation ${ x }^{ 2 }+bx+72=0$ has two distinct integer roots, then the number of all possible values of $b$ is
Question 17 :
Let $a, b$ and $c$ be three real numbers, such that $a+2b+4c=0$. Then the equation $a{ x }^{ 2 }+bx+c=0$
Question 18 :
Let $f(x)$ be a quadratic polynomial with $f(2)=10$ and $f(-2)=-2$. Then the coefficient of x in $f(x)$ is $?$<br>
Question 19 :
If $x+y+z = 0$ then what is the value of<br/>$\dfrac{1}{x^2 + y^2 - z^2} + \dfrac{1}{y^2 + z^2 - x^2} + \dfrac{1}{z^2 + x^2 - y^2}$<br/>
Question 20 :
If ${ x }^{ 2 }+{ y }^{ 2 }-4x-2y+5=0$ and ${ x }^{ 2 }+{ y }^{ 2 }-6x-4y-3=0$ are members of a coaxal system of circles then centre of a point circle in the system is
Question 21 :
Find the term independent of x in the expansion of $\left(2x^2-\dfrac{3}{x^3}\right)^{25}$.
Question 22 :
If $|2x + 3|\le 9$ and $2x + 3 < 0$, then
Question 23 :
For what value of $k$ is $x^2 + kx + 9=(x+3)^2$?
