Question Text
Question 1 :
The zeroes of $3x^4+6x^3–2x^2–10x–5$ are $\sqrt{\frac{5}{3}}$, $-\sqrt{\frac{5}{3}}$, -1 and -1. Is it true or false?
Question 2 :
Find the zeroes of the quadratic polynomial $2x^{2} - 8x + 6$.
Question 3 :
The zeroes of the polynomial $x^4-6x^3-26x^2-138x-35$ are $2\pm \sqrt {3}$, 7, -5.
Question 4 :
State true or false: If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Question 5 :
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given: $-\frac{8}{3}$, $\frac{4}{3}$
Question 6 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $\frac{21}{8}$, $\frac{5}{16}$
Question 7 :
Which of the following is not the graph of a quadratic polynomial?
Question 8 :
Divide $3x^{3}+x^{2}+2x+5$ by $1+2x+x^{2}$. The quotient is $3x–5$ and the remainder is $9x+10$. Is it correct?
Question 9 :
For which values of a and b, are the zeroes of $q\left(x\right)=x^3+2x^2+a$ also the zeroes of the polynomial $p\left(x\right)=x^5-x^4-4x^3+3x^2+3x+b$?
Question 10 :
State true or false: If α and β are the zeroes of a quadratic polynomial $ax^{2}+bx+c$, then $α+β=-\frac{b}{a}$, $αβ=\frac{c}{a}$.