Question

The equation ax²+bx-9=0 has two distinct roots. The sum and the product of the roots are given in this table: Sum 8/9; Product -1 . Find the value of the coefficients a and b​

Answer 1

Step-by-step explanation:

Let the 2 roots be x and y

x + y =8/9 --- 1

xy =-1

x =-1/y --- 2

Substitute 2 on 1:

-1/y + y =8/9

-1 + y^2/y =8/9

-9 + 9y^2 =8y

9y^2 - 8y - 9 =0

- 27 /y

-81

+7/y

-8

Answer 2

Answer:

9 = a

b = -8

Step-by-step explanation:

Given:

ax²+bx-9=0

Sum of the roots =8/9

product of the roots =-1

To find :  

the value of the coefficients a and b​

Formula used :

Sum of the roots = -coefficient of x/coefficient of x^2

Product of roots = constant /coefficient of x^2

Solution =

Sum of the roots =8/9

-b/a=8/9

product of the roots =-1

-9/a = -1

9 = a

now put 9 = a in -b/a=8/9 :-

-b/9 = 8/9

b = -8

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