Question

If x = $\frac{2}{3}$ and x = -3 are roots of the quadratic equation ax² +7x +b =o, find the values of a and b.

Answer 1

Solution :

Given Quadratic equation :

ax² + 7x + b = 0 ---( 1 )

And x = 2/3 , x = -3 are roots of

equation ( 1 ) ,

Now ,

i ) Substitute x = 2/3 in equation ( 1 ),

we get

a(2/3)² + 7(2/3) + b = 0

=> 4a/9 + 14/3 + b = 0

Multiply each term by 9 , we get

=> 4a + 42 + 9b = 0

=> 4a + 9b = -42 ---( 2 )

ii ) Substitute x = -3 in equation ( 1 ),

we get

a(-3)² + 7(-3) + b = 0

=> 9a - 21 + b = 0

=> b = -9a + 21 ---( 3 )

Put b = -9a + 21 in equation ( 2 ),

4a + 9( -9a + 21 ) = -42

=> 4a - 81a + 189 = -42

=> - 77a = -42 - 189

=> -77a = - 231

=> a = ( -231 )/( -77 )

=> a = 3

Put a = 3 in equation ( 3 ), we get

b = - 9×3 + 21

=> b = -27 + 21

=> b = -6

Therefore ,

a = 3 , b = -6

•••••

Answer 2

hope this helps..........