Question types

Quadratic Equations question types

344 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

344
Questions
4
Question groups
5
Question types
Sample Questions

Quadratic Equations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

If sin $\alpha$ and $\cos\alpha$ are the roots of the equations $ax^2+ bx + c = 0,$ then $b^2=$
  • A
    $ a^2-2 a c $
     
  • $ a^2+2 a c$
     
  • C
    $ a^2-a c $
     
  • D
    $a 2+a c $

Answer: B.

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If $2$ is a root of the equation $x^2+ bx + 12 = 0$ and the equation $x^2+ bx + q = 0$ has equal roots, then $q =$
  • A
    $8$
     
  • B
    $-8$
     
  • $16$
     
  • D
    $-16$

Answer: C.

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If the equation $x^2+4 x+k=0$ has real and distinct roots, then:
  • $\text{k}<4$
     
  • B
    $\text{k}>4$
     
  • C
    $\text{k}\geq4$
     
  • D
    $\text{k}\leq4$

Answer: A.

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The value of $c$ for which the equation $ax^2+ 2bx + c = 0$ has equal roots is:
  • $\frac{\text{b}^2}{\text{a}}$
     
  • B
    $\frac{\text{b}^2}{4\text{a}}$
     
  • C
    $\frac{\text{a}^2}{\text{b}}$
     
  • D
    $\frac{\text{a}^2}{4\text{b}}$

Answer: A.

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Find the value of p for which quadratic equation $(p+1) x^2-6(p+1) x+3(p+9)=0$, $\text{p}\neq-1$ has equal roots. Hence, find the roots of the equation.
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Some students planned a picnic. The budget for food was Rs. $480$. But eight of these failed to go and thus the cost of food for each member increased by Rs. $10$. How many students attended the picnic?
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Out of a group of swans, $\frac{7}{2}$ times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
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Prove that both the roots of the equation $(x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0$ are real but they are equal only when $a = b = c.$
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