Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

Q. The quadratic polynomial whose sum and product of the zeroes is 9 and $\frac{1}{9}$ respectively is .

1. x2+9x-19
2. x2-9x+19
3. -x2-9x+19
4. 9x2-9x+19

Q. The quadratic polynomial whose sum and product of the zeroes is 9 and $\frac{1}{9}$ respectively is .

1. x2-9x+19
2. x2+9x-19
3. -x2-9x+19
4. 9x2-9x+19

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 quadratic polynomial whose sum of its zeroes (roots) is $-\frac{8}{5}$ and the product of the zeroes (roots) is $\frac{7}{5}$.

1. $14x^2+7x+5$

2. $5x^2+8x+7$

3. $2x^2-8x+7$

4. $5x^2-8x+7$

Q. The polynomial whose zeroes are $\frac{5+\sqrt{3}}{3},\frac{5-\sqrt{3}}{3}$ is .

1. 9x2-30x+22
2. 9x2+30x+22
3. x2+30x+22

Q.

If $\alpha ,\beta$ are the zeroes of the polynomial $x^2-px+36$ and ${\alpha }^2$+${\beta }^2$ = 9, then what is the value of p?

1. ±6

2. ±3

3. ±8

4. ±9

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 -2 and -4 are the zeroes of a quadratic polynomial whose leading coefficient is 2, then find the value of (product of zeroes $\times$ coefficient of x).

[Note: In a polynomial, the term containing the highest power of x (i.e. a_nxⁿ) is the leading term, and we call a_n the leading coefficient.]

1. 96
2. -96
3. 16
4. -16

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.

Find a quadratic polynomial with $\frac{1}{8}$ as the sum and 2 as product of its zeroes.

1. $8x^2+x+16$

2. $8x^2-x+16$

3. $8x^2-x-16$

4. $8x^2+x-16$