# SUM AND PRODUCT OF ROOTS OF QUADRATIC EQUATION WORKSHEET

Sum and Product of Roots of Quadratic Equation Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on sum and product of the roots of a quadratic equation.

Before look at the worksheet, if you would like to learn how to find the sum and product of the roots of a quadratic equation,

## Sum and Product of Roots of Quadratic Equation Worksheet - Problems

Problem 1 :

Find the sum and product of roots of the quadratic equation given below.

x2 - 5x + 6  =  0

Problem 2 :

Find the sum and product of roots of the quadratic equation given below.

x2 - 6  =  0

Problem 3 :

Find the sum and product of roots of the quadratic equation given below.

3x2 + x + 1  =  0

Problem 4 :

Find the sum and product of roots of the quadratic equation given below.

3x2 + 7x  =  2x - 5

Problem 5 :

Find the sum and product of roots of the quadratic equation given below.

3x2 -7x + 6  =  6

Problem 6 :

Find the sum and product of roots of the quadratic equation given below.

x2 + 5x + 1  =  3x2 + 6

Problem 7 :

If the product of roots of the quadratic equation given below is 4, then find the value of m.

2x2 + 8x - m3  =  0

Problem 8 :

If the sum of roots of the quadratic equation given below is 0, then find the value of p.

x2 -(p + 4)x + 5  =  0

Problem 9 :

If the product of roots of the quadratic equation given below is 1, then find the value of m.

x2 + (2p - 1)x + p2  =  0

Problem 10 :

Find the sum and product of roots of the quadratic equation given below.

1/(x+1)  +  2/(x-4)  =  2 ## Sum and Product of Roots of Quadratic Equation Worksheet - Solutions

Problem 1 :

Find the sum and product of roots of the quadratic equation given below.

x2 - 5x + 6  =  0

Solution :

Comparing

x2 - 5x + 6  =  0

and

ax2 + bx + c  =  0

we get

a  =  1, b  =  -5 and c  =  6

Therefore,

Sum of the roots  =  -b/a  =  -(-5)/1  =  5

Product of the roots  =  c/a  =  6/1  =  6

Problem 2 :

Find the sum and product of roots of the quadratic equation given below.

x2 - 6  =  0

Solution :

Comparing

x2 - 6  =  0

and

ax2 + bx + c  =  0

we get

a  =  1, b  =  0 and c  =  -6

Therefore,

Sum of the roots  =  -b/a  =  0/1  =  0

Product of the roots  =  c/a  =  -6/1  =  -6

Problem 3 :

Find the sum and product of roots of the quadratic equation given below.

3x2 + x + 1  =  0

Solution :

Comparing

3x2 + x + 1  =  0

and

ax2 + bx + c  =  0

we get

a  =  3, b  =  1 and c  =  1

Therefore,

Sum of the roots  =  -b/a  =  -1/3

Product of the roots  =  c/a  =  1/3

Problem 4 :

Find the sum and product of roots of the quadratic equation given below.

3x2 + 7x  =  2x - 5

Solution :

First write the given quadratic equation in standard form.

3x2 +7x  =  2x - 5

3x2 + 5x + 5  =  0

Comparing

3x2 + 5x + 5  =  0

and

ax2 + bx + c  =  0

we get

a  =  3, b  =  5 and c  =  5

Therefore,

Sum of the roots  =  -b/a  =  -5/3

Product of the roots  =  c/a  =  5/3

Problem 5 :

Find the sum and product of roots of the quadratic equation given below.

3x2 -7x + 6  =  6

Solution :

First write the given quadratic equation in standard form.

3x2 -7x + 6  =  6

3x2 - 7x  =  0

Comparing

3x2 - 7x  =  0

and

ax2 + bx + c  =  0

we get

a  =  3, b  =  -7 and c  =  0

Therefore,

Sum of the roots  =  -b/a  =  -(-7)/3  =  7/3

Product of the roots  =  c/a  =  0/3  =  0

Problem 6 :

Find the sum and product of roots of the quadratic equation given below.

x2 + 5x + 1  =  3x2 + 6

Solution :

First write the given quadratic equation in standard form.

x2 + 5x + 1  =  3x² + 6

0  =  2x2 - 5x + 5

2x2 - 5x + 5  =  0

Comparing

2x2 - 5x + 5  =  0

and

ax2 + bx + c  =  0

we get

a  =  2, b  =  -5 and c  =  5

Therefore,

Sum of the roots  =  -b/a  =  -(-5)/3  =  5/2

Product of the roots  =  c/a  =  5/2

Problem 7 :

If the product of roots of the quadratic equation given below is 4, then find the value of m.

2x2 + 8x - m3  =  0

Solution :

Comparing

2x2 + 8x - m3  =  0

and

ax2 + bx + c  =  0

we get

a  =  2, b  =  8 and c  =  -m3

Given : Product of the roots is 4.

Then,

c/a  =  4

-m3/2  =  4

Multiply each side by (-2).

m3  =  -8

m3  =  (-2)3

m  =  -2

Problem 8 :

If the sum of roots of the quadratic equation given below is 0, then find the value of p.

x2 -(p + 4)x + 5  =  0

Solution :

Comparing

x2 -(p + 4)x + 5  =  0

and

ax2 + bx + c  =  0

we get

a  =  1, b  =  -(p + 4) and c  =  5

Given : Sum of the roots is 0.

Then,

-b/a  =  0

-[-(p + 4)]  =  0

(p + 4)  =  0

p + 4  =  0

p  =  -4

Problem 9 :

If the product of roots of the quadratic equation given below is 1, then find the value of m.

x2 + (2p - 1)x + p2  =  0

Solution :

Comparing

x2 + (2p - 1)x + p2  =  0

and

ax2 + bx + c  =  0

we get

a  =  1, b  =  (2p - 1) and c  =  p2

Given : Product of the roots is 1.

Then,

c/a  =  1

p2/1  =  1

p2  =  1

Take square root on both sides.

p2  =  √1

p  =  ±1

Problem 10 :

Find the sum and product of roots of the quadratic equation given below.

1/(x+1)  +  2/(x-4)  =  2

Solution :

First write the given quadratic equation in standard form.

1/(x+1)  +  2/(x-4)  =  2

[1(x-4) + 2(x+1)] / [(x+1)(x-4)]  =  2

1(x-4) + 2(x+1)  =  2(x+1)(x-4)

x - 4 + 2x + 2  =  2(x2 - 4x + x - 4)

3x - 2  =  2(x2 - 3x - 4)

3x - 2  =  2x2 - 6x - 8

0  =  2x2 - 9x - 6

2x2 - 9x - 6  =  0

Comparing

2x2 - 9x - 6  =  0

and

ax2 + bx + c  =  0

we get

a  =  2, b  =  -9 and c  =  -6

Therefore,

Sum of the roots  =  -b/a  =  -(-9)/2  =  9/2

Product of the roots  =  c/a  =  -6/2  =  -3 After having gone through the stuff given above, we hope that the students would have understood how find the sum and product of the roots of a quadratic equation without solving the equation.

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