Relationship Between Zeroes and Coefficients of a Polynomial

Q.

Find the zeros of the following quadratic polynomials $6x^2-3-7x$ and verify the relationship between the zeros and the coefficients.

Q.

Find the zeroes of the quadratic polynomial $4x^2-4x-3$ and verify the relationship between the zeroes and the coefficients of the polynomial.

Q. Find the sum of roots and product of roots respectively for the polynomial :
$2x^2+x-5=0$

1. $-\frac{1}{2},\frac{5}{2}$
2. 2, 5
3. $-\frac{1}{2},-\frac{5}{2}$
4. $-\frac{1}{2},\frac{5}{2}$

Q. The product of zeros of cubic polynomial $x^3-3x^2-x+3$ is

1. -3
2. -1
3. 3
4. 1

Q.

The sum of all zeroes of the polynomial p(x) = $5x^5-20x^4+5x^3+50x^2-20x-40$ is

___

and the product is

___ .

Q. Is the following statement true or false? Justify your answers.
If all the three zeroes of a cubic polynomial $x^3+a{x}^2-bx+c$ are positive, then at least one of a, b and c is non-negative.

1. True
2. False

Q. $\text{Find the sum and product of roots of the}\text{polynomial}2x^2+x-5=0.$

1. $-\frac{1}{2},\frac{5}{2}$
2. 2, 5
3. $-\frac{1}{2},-\frac{5}{2}$
4. $-\frac{1}{2},\frac{5}{2}$

Q. $aandb$ are the zeroes of a quadratic polynomial $p\left(x\right)$, and $k$ is any constant. Then general form of polynomial is.

1. $k{x}^2+(a+b)x+ab$
2. $k{x}^2+k(a+b)x+kab$
3. $k{x}^2-k(a+b)x+kab$

Q. If $\alpha ,\beta ,\gamma$ are the zeroes of a cubic polynomial $a{x}^3+b{x}^2+cx+d$, then the sum of products of the zeroes taken two at a time is equal to

1. $\alpha -\beta -\gamma =\frac{c}{a}$
2. $\alpha .\beta .\gamma =\frac{c}{a}$
3. $\alpha +\beta +\gamma =\frac{-d}{a}$
4. $\alpha \beta +\beta \gamma +\alpha \gamma =\frac{c}{a}$

Q. Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.

1. $x^2-2x-24$
2. $x^2-10x+25$
3. $64x^2-1$
4. $x^2+x-30$

Q. Find the sum and product of zeroes of polynomials $2x^2-8x+6$.