Mathematics

Eleven Standard

Test your understanding of this lesson Quadratic equation important properties:-

1)
If \(2+\sqrt{3}\) is a root of the quadratic equation \(x^{2}-4x+1=0\) then other root is
  • \(-2+\sqrt{3}\)
  • \(-2-\sqrt{3}\)
  • \(2-\sqrt{3}\)
  • none of these
2)
If a+b+c=0 and a,b,c are rational, then the roots of the equation \((b+c-a)x^{2}+(c+a-b)x+(a+b-c)=0\) are
  • rational
  • irrational
  • imaginary
  • equal
3)
If the roots of the equation \(\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}\) are equal in magnitude but opposite in sign, then their product is
  • -\(\frac{1}{2}(a^{2}+b^{2})\)
  • \(\frac{1}{2}ab\)
  • -\(\frac{1}{2}ab\)
  • \(\frac{1}{2}(a^{2}+b^{2})\)
4)
If x is real, then the maximum value of \(3-6x-8x^{2}\) is
  • \(\frac{17}{8}\)
  • \(\frac{33}{8}\)
  • \(\frac{21}{8}\)
  • \(\frac{27}{8}\)
5)
If the roots of the equation \(x^{2}-2ax+a^{2}+a-3=0\) are real and less than 3, then
  • a<2
  • \(2 \leq a \leq 3\)
  • \(3 \leq a \leq 4\)
  • a>4

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