Sum and Product of Roots

Sum and Product of Roots2If and are the roots of 0, then;ax bx c

Sum and Product of Roots2If and are the roots of 0, then;ax bx c

2ax bx c a x x

Sum and Product of Roots2If and are the roots of 0, then;ax bx c

2ax bx c a x x

2 2ax bx c a x x x

Sum and Product of Roots2If and are the roots of 0, then;ax bx c

2ax bx c a x x

2 2ax bx c a x x x

2 2b cx x x xa a

Sum and Product of Roots2If and are the roots of 0, then;ax bx c

2ax bx c a x x

2 2ax bx c a x x x

2 2b cx x x xa a

Thus

Sum and Product of Roots2If and are the roots of 0, then;ax bx c

2ax bx c a x x

2 2ax bx c a x x x

2 2b cx x x xa a

Thus (sum of roots)b

a

Sum and Product of Roots2If and are the roots of 0, then;ax bx c

2ax bx c a x x

2 2ax bx c a x x x

2 2b cx x x xa a

Thus (sum of roots)b

a

(product of roots)ca

e.g. (i) Form a quadratic equation whose roots are;

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4 4 5

1

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4 4 5

1

2 4 1 0x x

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4 4 5

1

2 4 1 0x x

2( ) If and are the roots of 2 3 1 0, find;ii x x

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4 4 5

1

2 4 1 0x x

2( ) If and are the roots of 2 3 1 0, find;ii x x

) a

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4 4 5

1

2 4 1 0x x

2( ) If and are the roots of 2 3 1 0, find;ii x x

) a

32

ba

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4 4 5

1

2 4 1 0x x

2( ) If and are the roots of 2 3 1 0, find;ii x x

) a

32

ba

) b

e.g. (i) Form a quadratic equation whose roots are;) 2 and 3a

1 6

2 6 0x x

) 2 5 and 2 5b 4 4 5

1

2 4 1 0x x

2( ) If and are the roots of 2 3 1 0, find;ii x x

) a

32

ba

) b

12

ca

2 2) c

2 2) c 2 2

2 2) c 2 2 23 12

2 2

2 2) c 2 2 23 12

2 2

9 14134

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2

2 6

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2

2 6

3 62

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2

2 6 2 m

3 62

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2

2 6 2 m

3 62

22 m

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2

2 6 2 m

3 62

22 m 22 2 m

2 2) c 2 2 23 12

2 2

9 14134

1 1) d

321

2

3

2( ) Find the value of if one root is double the other in 6 0iii m x x m Let the roots be and 2

2 6 2 m

3 62

22 m 22 2 m

8m

2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x

2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x

1Let the roots be and

2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x

1Let the roots be and

1 12 1m

2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x

1Let the roots be and

1 12 1m

112 1m

2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x

1Let the roots be and

1 12 1m

112 1m

2 1 12 2

1

mmm

2( ) Find the values of in 2 1 1 1 0, if one root is the reciprocal of the other.iv m m x m x

1Let the roots be and

1 12 1m

112 1m

Exercise 8H; 3beh, 4bdf, 5, 6, 7abc i, 8, 10, 12,13cd, 15, 18, 20, 21ac

2 1 12 2

1

mmm