Polynomials Quiz 4

Question 1

If $\alpha,\beta$ are the two zeroes of the polynomial f(x) = $x^2-p(x+1)-c,$ then $(\alpha+1)(\beta+1)$ = &hellip;&hellip;&hellip;&hellip;&hellip;

Accepted Answer

1 - c

Answer

c - 1

Answer

c

Answer

1 + c

Question 2

If $\alpha$ and $\beta$ are the roots of $ax^2+bx+c=0$, then $\alpha^3+\beta^3$ =

Accepted Answer

$\frac{3abc-b^3}{a^3}$

Answer

$\frac{3abc-b^3}{c^3}$

Answer

$\frac{b^2-3abc}{a^3}$

Answer

$\frac{b^2-3abc}{c^3}$

Question 3

The equation whose roots are obtained by adding 1 to those of $2x^2$+ 3x + 5 = 0 is

Accepted Answer

$2x^2$ &ndash; x + 4 = 0

Answer

$2x^2$ &ndash; x &ndash; 4 = 0

Answer

$2x^2$ + x &ndash; 4 = 0

Answer

None of these

Question 4

If x+1, x+2 are two factors of $x^3+3x^2-2\alpha x+\beta,$ then value of $\alpha+\beta$ is &hellip;&hellip;&hellip;&hellip;

Accepted Answer

-1

Answer

1

Answer

-2

Answer

2

Question 5

If $\alpha,\beta$ are zeroes of the polynomial $ax^2+bx+c,$ then the value of $\frac{1}{\alpha}+\frac{1}{\beta}$ is&hellip;&hellip;&hellip;&hellip;

Accepted Answer

$\frac{-b}{c}$

Answer

$\frac{-b}{ac}$

Answer

b = ac

Answer

$-\sqrt\frac{b}{ac}$

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