R. D. Sharma Solutions for Chapter: Polynomials, Exercise 4: VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

Write the standard form of a linear polynomial with real coefficients.

The sum and product of the zeros of a quadratic polynomial are $-\frac{1}{2}$ and $-3$, respectively. What is the quadratic polynomial.

If $(x+a)$ is a factor of $2x^2+2ax+5x+10$, find $a.$

If a quadratic polynomial $f\left(x\right)$ is a square of a linear polynomial, then its two zeroes are coincident.

If a quadratic polynomial $f\left(x\right)$ is not factorizable into linear factors, then it has no real zero.

If $f\left(x\right)$ is a polynomial such that $f\left(a\right)f\left(b\right)<0$, then what is the number of zeros lying between $a$ and $b$?

If the graph of quadratic polynomial $a{x}^2+bx+c$ cuts the positive direction of $y\mathit{-}axis$, then what is the sign of $c$?   

If the graph of quadratic polynomial $a{x}^2+bx+c$ cuts negative direction of $y-\text{axis}$, then what is the sign of $c$?