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