Question types

Quadratic Equations question types

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

413
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 $a x^2+b x+c=0$, 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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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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