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.
If $p-15=0$ and $2 x^2+p x+25=0$;find the values of $x$.
View full solution →Solve $3 \sqrt{2 x^2}-5 x-\sqrt{2}=0$
View full solution →Find, using quadratic formula, the roots of the following quadratic equations, if they exist
$x^2+4 x+5=0$
View full solution →Find the value of k for which equation $4 x^2+8 x-k=0$ has real roots.
View full solution →Solve :
$(x+5)(x-5)=24$
View full solution →Find the value of m for which the equation $(m+4) x^2+(m+1) x+1=0$ has real and equal roots.
View full solution →Solve the quadratic equation $8 x^2-14 x+3=0$
(i) When $x \in I$ (integers)
(ii) When $x \in Q$ (rational numbers)
View full solution →Find the solution of the equation $2 x^2-m x-25 n=0$ if $m + 5 = 0$ and $n - 1 = 0$
View full solution →Solve $(x-10)\left(\frac{1200}{x}+2\right)=1260$ and $x<0$.
View full solution →Solve : $\frac{1}{18-x}-\frac{1}{18+x}=\frac{1}{24}$ and $x > 0$
View full solution →Solve, using formula :$x^2+x-(a+2)(a+1)=0$
View full solution →If m and n are roots of the equation $\frac{1}{x}-\frac{1}{x-2}=3$ where x ≠ 0 and x ≠ 2; find m × n.
View full solution →One root of the quadratic equation $8 x^2+m x+15=0$ is $\frac{3}{4}$ Find the value of m. Also, find the other root of the equation.
View full solution →Solve: $2 x-3=\sqrt{2 x^2-2 x+21}$
View full solution →Solve $2\left(x^2+\frac{1}{x^2}\right)-\left(x+\frac{1}{x}\right)=11$
View full solution →If 3 is a root of the quadratic equation $x^2-p x+3=0$ then $p$ is equal to:
Answer: A.
View full solution →The roots of the quadratic equation $p x^2-q x+r=0$ are real and equal if:
- A
$p^2=4 q r$
- ✓
$q^2=4 p r$
- C
$-q^2=4 p r$
- D
$p^2 > 4 p r$
Answer: B.
View full solution →Which of the following is/are correct?
Statement (A): The equation $x^2-3 x-10=0$ has two roots i.e., -2 and 5 .
Statement (B): The discriminant of the quadratic equation $3 x^2-5 x-12=0$ is 144 .
Statement (C): $\sqrt{2}$ is solution of the quardratic equation. $x^2+\sqrt{2} x-4=0$
- A
- B
- ✓
- D
All A, B and C are correct
Answer: C.
View full solution →Which of the following is/are correct?
Statement (A): Two real and different roots if and if $b^2>4 a c$
Statement (B): Two real roots if and only if $b^2 \geq 4 a c$.
Statement (C): no real roots if and only if $b^2=4 a c$
- ✓
- B
- C
- D
All A, B and C are correct
Answer: A.
View full solution →Statement (A): If one root of the quadratic equation $6 x^2-x-k=0$ is $\frac{2}{3}$, then the value of $k$ is 2 .
Statement (B): The quadratic equation $a x^2+b x+c=0, a \neq 0$ has almost two roots.
Which of the statement is valid?
Answer: C.
View full solution →Assertion : The roots of the equation $x^2+3 x+7=0$ are imaginary.
Reason : If discriminant (D) of a quadratic equation is less than zero, then the roots of the quadratic equation are imaginary.
- ✓
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: A.
View full solution →Assertion : A natural number, when increased by 12 , equals 160 times its reciprocal. The number is 20 .
Reason : The roots of a quadratic equation $a x^2+b x+c=0$ are given by the formula $x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- ✓
Assertion is incorrect but reason is correct.
Answer: D.
View full solution →Assertion: The values of $k$ for which the equation $k x^2+1-2(k-1) x+x^2=0$ has equal roots are 0,3 .
Reason : If the roots of a quadratic equation are equal, then its discriminant is greater than zero.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- ✓
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: C.
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