Polynomial: Grade 10

If (x–1) is a factor of  $k^3x^3-4kx+4k-1$ then the value of k is- 

• 1

• -1

• 2

• -2

Quadratic polynomial having zeros 1 and –2 is –

•  $x^2-x+2$  

•  $x^2-x-2$  

•  $x^2+x-2$  

• None of these

If one of the factors of $x^2+x–20$ is (x–5) then other factor is –

• (x–4)

• (x–5)

• (x–6)

• (x–7)

If  $\alpha,\ \beta$   be the zeros of the quadratic polynomial  $2x^2+5x+1$ then the value of  $\alpha+\beta+\alpha\beta$   

• –2

• –1

• 1

• None of these

Quadratic polynomial having sum of it's zeros 5 and product of it's zeros – 14 is –

•  $x^2-5x-14$  

•  $x^2-10x-14$  

•  $x^2-5x+14$  

• None of these

If x = 2 and x = 3 are zeros of the quadratic polynomial $x^2+ax+b$ the values of a and b respectively are :

• 5, 6

• –5, –6

• –5, 6

• 5, –6

Let $p\left(x\right)=ax^3+bx-c$ be a cubic polynomial. It can have at most –

• One zero

• Two zero

• Three zero

• None of these

 If $\alpha$ and  $\beta$  are the zeros of the polynomial  $f\left(x\right)=16x^2+4x-5$  then  $\frac{1}{\alpha}+\frac{1}{\beta}$  is equal to –

•  $\frac{2}{5}$  

•  $\frac{5}{2}$  

•  $\frac{3}{5}$  

•  $\frac{4}{5}$  

 

If  $\alpha$   and  $\beta$   are the zeros of the polynomial  $6x^2-3-7x$   then $\left(\alpha+1\right)\left(\beta+1\right)$ is equal to –

•  $\frac{5}{2}$  

•  $\frac{5}{3}$  

•  $\frac{2}{5}$  

•  $\frac{3}{5}$  

If the polynomial  $3x^2-x^3-3x+5$    is divided by another polynomial $x-1-x^2$ , the remainder comes out to be 3, then quotient polynomial is –

• 2 – x

• 2x – 1

• 3x + 4

• x – 2