Question types

Quadratic Equations question types

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

345
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
    $a^2 - 2ac$
  • $a^2 + 2ac$
  • C
    $a^2 - ac$
  • D
    $a2 + ac$

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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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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If the roots the equations $ax^2 + 2bx + c = 0$ and $\text{bx}^2-2\sqrt{\text{ac}}\text{x}+\text{b}=0$ are simultaneously real, then prove that $b^2 = ac.$
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A pole has to be erected at a point on the boundary of a circular park of diameter $13$ meters in such a way that the difference of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7$ meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
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A two-digit number is such that the product of digit is 12. When 36 is added to the number the digits interchange their places. Determine the number.
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