Relationship Between Roots and Coefficients of Quadratic Equation

Q. The sum and product of zeroes of a quadratic polynomial $a{x}^2+bx+c$ respectively are and .

1. -ba
2. ca
3. ba
4. -ca

Q. If $x$ and $y$ are the roots of the polynomial $4k^2+5k+6$, then match the follwing with their values.

1. $-\frac{5}{4}$
2. $\frac{3}{2}$
3. $-\frac{5}{6}$

Q. If p and q are the roots of $2x^2+3x+4$ = 0, them $p^{2}q+q^{2}p$ = .

1. -3
2. -4
3. 8
4. 16

Q. Arrange the following equations based on the ascending order of sum of their roots.(Top to bottom direction)

1. $x^2-6x+8=0$
2. $x^2-4x+4=0$
3. $x^2-8x+16=0$
4. $x^2-2x+1=0$

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

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

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. Find the quadratic equation whose sum of roots is 5 and whose product of roots is 6.

1. $x^2+5x+6$
2. $x^2-5x+6$
3. $x^2+6x+5$
4. $x^2-6x+5$

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. If $\alpha \&\beta$ are the zeroes of a quadratic polynomial p(x), and k is any constant, then what is the general form of the polynomial?

1. $k\left[x^2-(\alpha +\beta )x+\alpha \beta \right]$
2. $k{x}^2-(\alpha +\beta )x-\alpha \beta$
3. $k{x}^2+(\alpha +\beta )x-\alpha \beta$
4. $k^2{x}^2+k(\alpha +\beta )x+k\alpha \beta$

Q. If $\alpha \text{and}\beta$ are the zeroes of $p\left(x\right)=4x^2+10x+k$ such that ${\alpha }^2+{\beta }^2+\alpha \beta =\frac{21}{4}$, then k =

1. 12
2. 4
3. 2
4. - 12