# Sum and Product of Roots of a Quadratic Equation

## Trending Questions

**Q.**

Find the zeros of the following quadratic polynomials $4{s}^{2}-4s+1$ and verify the relationship between the zeros and the coefficients.

**Q.**

Find the quadratic polynomial, sum of whose zeros is (52) and their product is 1. Hence, find the zeros of the polynomial?

**Q.**

If x=23 and x=−3 are the roots of the quadratic equation ax2+7x+b=0 then find the values of a and b.

**Q.**

$\text{Findthezeroesofthepolynomial}p\left(x\right)=4{x}^{2}-4x+1\text{andverifytherelationshipbetweenthezeroesandthecoefficients.}$

**Q.**

If the sum of the zeros of the quadratic polynomial kx2+2x+3k is equal to the product of its zeros then k = ?

(a) 13 (b) −13 (c) 23 (d) −23

**Q.**

The zeros of the quadratic polynomial x2+88x+125 are

(a) both positive (b) both negative

(c) one positive and one negative (d) both equal

**Q.**

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.

(i) −83, 43 (ii) 218, 516 (iii) −2√3, −9 (iv) −32√5, −12

**Q.**

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

5x2−4−8x

**Q.**

Find the quadratic polynomial, the sum of whose zeros is 0 and their product is -1. Hence, find the zeros of the polynomial.

**Q.**

If the product of the roots of x2–3x+k=10 is –2, then find the value of k.

-2

8

12

6

**Q.**

**Question 2 (i)**

Are the following statements ‘True’ or False’? Justify your answer.

i) If the zeroes of a quadratic polynomial ax2+bx+c are positive then a, b and c all have the same sign.

**Q.**Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.

t2−15

**Q.**

The sum and the product of the zeros of a quadratic polynomial are 3 and -10 respectively. The quadratic polynomial is

(a) x2−3x+10 (b) x2+3x−10 (c) x2−3x−10 (d) x2+3x+10

**Q.**

Find the zeroes of the following polynomial by factorization method: $3{x}^{2}+4x-4$.

**Q.**Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.

4s2−4s+1

**Q.**

If one zero of the polynomial $\left({a}^{2}+2\right){x}^{2}+10x+3a$ is the reciprocal of the other. find $a$.

**Q.**

If the sum of the roots of a quadratic equation is 5 and the product of the roots is also 5, then the equation can be:

**Q.**The roots of the quadratic equation 3x2+2x−1=0 are

- 1, 13
- -1, 13
- 2, 3
- -2, 13

**Q.**

For the same amount of work, A takes 6 hours less than B. If together they complete the work in 13 hours 20 minutes, find how much time will B alone take to complete the work?

40 hrs

10 hrs

15 hrs

30 hrs

**Q.**Question 1 (iv)

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.

iv) =−32√5, −12

**Q.**

If the product of the roots of x2–3x+k=10 is –2, then find the value of k.

-2

8

12

6

**Q.**

Question 1 (v)

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

t2−15

**Q.**

The sum of two numbers is 48 and their product is 432 Find the numbers.

**Q.**

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

2x2−11x+15

**Q.**

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients :

2√3x2−5x+√3

**Q.**Question 1 (x)

Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials

(x) 7y2–113y−23

**Q.**

Question 1 (ii)

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

4s2−4s+1

**Q.**

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

4x2−4x−3

**Q.**

Find the values of k for which the given quadratic equation has real and distinct roots:

(i)kx2+2x+1=0 (ii)kx2+6x+1=0

**Q.**Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.

6x2−3−7x