CAT Quadratic Equations Practice Questions With Solutions

If $\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$, then $\sqrt{10x+9}$ is equal to

If $x$ and $y$ are real numbers such that $x^{2} + (x - 2y - 1)^{2} = -4y(x + y)$, then the value $x - 2y$ is

The sum of all possible values of x satisfying the equation $2^{4x^{2}}-2^{2x^{2}+x+16}+2^{2x+30}=0$, is

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

If $p^{2}+q^{2}-29=2pq-20=52-2pq$, then the difference between the maximum and minimum possible value of $(p^{3}-q^{3})$

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is $(n + 2n^2)$. If the $n^{th}$ term of the progression is divisible by 9, then the smallest possible value of n is

Let a, b, c be non-zero real numbers such that $b^2 < 4ac$, and $f(x) = ax^2 + bx + c$. If the set S consists of all integers m such that f(m) < 0, then the set S must necessarily be

Let a and b be natural numbers. If $a^2 + ab + a = 14$ and $b^2 + ab + b = 28$, then $(2a + b)$ equals

Let $f(x)$ be a quadratic polynomial in $x$ such that $f(x) \geq 0$ for all real numbers $x$. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to

Let r and c be real numbers. If r and -r are roots of $5x^{3} + cx^{2} - 10x + 9 = 0$, then c equals