Sample QuestionsQuadratic Equations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The ratio of the sum and product of the roots of the equation $7x^2- 12x + 18 = 0$ is:
- A
$7 : 12$
- B
$7 : 18$
- C
$3 : 2$
- ✓
$2 : 3$
Answer: D.
View full solution →If the equation $x^2 - kx + 1 = 0$ has no real roots, then:
- A
$k < -2$
- B
$k > 2$
- ✓
$-2 < k < 2$
- D
Answer: C.
View full solution →If $x = 3$ is a solution of the equation $3x^2 + (k - 1)x + 9 = 0$ then $k =$ ?
Answer: B.
View full solution →If the product of the roots of the equation $x^2 - 3x + k = 10$ is $-2$ then the value of k is:
Answer: C.
View full solution →If the equation $x^2 + 5kx + 16 = 0$ has no real roots then:
Answer: C.
View full solution →Solve the following quadratic equation:$\sqrt7\text{x}^2-\text{6x}-13\sqrt7=0$
View full solution →Find the value of $\alpha$ for which the equation $(\alpha+12)\text{x}^2+2(\alpha-12)\text{x}+2=0$ has equal roots.
View full solution →Find the discriminant of the following equation:
$(x - 1)(2x - 1) = 0$
View full solution →Find the roots of the following equations, if they exist, by applying the quadratic formula:
$25x^2 + 30x + 7 = 0$
View full solution →The following are quadratic equations in x?$(2x + 3)(3x + 2) = 6(x - 1)(x - 2)$
View full solution →Solve the following quadratic equation:$3\text{x}^2-2\sqrt6\text{x}+2=0$
View full solution →Solve the following quadratic equation:
$x^2 + 5x - (a^2 + a - 6) = 0$
View full solution →Solve the following quadratic equation: $x^2 - (2b - 1)x + (b^2 - b - 20) = 0$
View full solution →Solve the following quadratic equation: $2x^2 + ax - a^2 = 0$
View full solution →If $-4$ is a root of the quadratic equation $x^2 + 2x + 4p = 0$, find the value of $k$ for which the quadratic equation $x^2 + px(1 + 3k) + 7(3 + 2k) = 0$ has equal roots.
View full solution →The sum of the reciprocals of Meena's ages (in years) $3$ years ago and $5$ years hence is $\frac{1}{3}.$ Find her present age.
View full solution →A teacher on attempting to arrange the students for mass drill in the form of a solid square found that $24$ students were left. When he increased the size of the square by one student, he found that he was short of $25$ students. Find the number of students.
View full solution →Solve the following equations by using the method of completing the square:
$3x^2 - 2x - 1 = 0$
View full solution →Solve the following equations by using the method of completing the square:
$2x^2 + 5x - 3 = 0$
View full solution →The product of Tanvy's age (in years) $5$ years ago and her age $8$ years later is $30$. Find her present age.
View full solution →Find the values of k so that the quadratic equation $9x^2- 3kx + k = 0$ has equal roots.
View full solution →If $1$ is a root of the equation $ay^2 + ay + 3 = 0$ and $y^2 + y + b = 0$ then find the value of ab.
View full solution →If one root of the quadratic equation $3x^2 - 10x + k = 0$ is reciprocal of the other, find the value of $k$.
View full solution →Show that $x = -3$ is a solution of $x^2 + 6x + 9 = 0$.
View full solution →The sum of two natural numbers is $8$ and their product is $15$. Find the numbers.
View full solution →Solve the following quadratic equation:
$\frac{4}{\text{x}}-3=\frac{5}{\text{2x}+3},$ $\text{x}\neq=0,\ \frac{-3}{2}$
View full solution →Find the roots of the following equation, if they exist, by applying the quadratic formula:$12abx^2 - (9a^2 - 8b^2)x - 6ab = 0$,
where $ \text{a}\neq0$ and $\text{b}\neq0$
View full solution →Find the roots of the following equation, if they exist, by applying the quadratic formula:
$a^2b^2x^2 - (4b^4 - 3a^4)x - 12a^2b^2 = 0$, $ \text{a}\neq0$ and $\text{b}\neq0$
View full solution →Solve the following quadratic equation:
$\frac{\text{x}-1}{\text{x}-2}+\frac{\text{x}-3}{\text{x}-4}=3\frac{1}{3},$
$\text{x}\neq2,4$
View full solution →Find the roots of the following equation, if they exist, by applying the quadratic formula:
$4x^2 - 4a^2x + (a^4 - b^4) = 0$
View full solution →