Algebra & Calculus

A polynomial of degree three is called

• Quadratic

• bi quadratic

• cubic

• linear

Choose the incorrect answer from the following.
    Every  nth degree equation f(x)=0  has ----------

• at least  n roots

• at most n  roots

• exactly  n roots

• at least one real root

  The equation   $x^7+8x^5-x+9=0$  has----------

• at most 3 real roots

• at most 4 imaginary roots

• exactly 7 roots, real or imaginary

• exactly 7 imaginary roots

The number of complex roots of x⁴ + 3x -1=0

• 0

• 2

• 3

• 1

The product of the roots of the equation x⁵-ax³+bx²+d=0 is -d

• True

• False

 If  $\alpha,\ \beta,\ \gamma$  are the roots of the equation   $$
x^3+ax-b=0  then the value of  $\sum_{ }^{ }\frac{\alpha}{\beta\gamma}$   is 2
  

• True

• False

One real root of the equation x³-7x²+14x-8=0 is

• 2

• -2

• 3

• -1

If one root of the equation x³- 3x² + 4x -2 = 0 is 1-i then the other imaginary root is

• -1-i

• -1+i

• 1+i

• 1-i

The roots of the equation $$x-\frac{2}{x}=1$$ are

• -1, 2

• 1, 2

• -1, -2

• 1, -2

For a cubic equation  $-ax^3-bx^2+cx-d=0$  the sum of the product of the roots 2 at a time is

•  $\frac{-c}{a}$  

•  $\frac{c}{a}$  

•  $\frac{-b}{a}$  

•  $\frac{d}{a}$