Question

19. If x = 2/3 and x = -3 are the roots of the quadratic equation ax*2+7x+b = 0
then find the values of a and b.
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Answer 1

Answer:

x=2/3 and x= -3 are roots.

they are factors of f(x) = ax^2+7x+b then it means that f(2/3) and f(-3) should be 0.

putting x= 2/3

f(2/3) = (a×2/3×2/3) +7(2/3)+b

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

4a/9+b = -14/3....(1)

putting x= -3

f(-3) = a(-3×-3)+7(-3)+b

= 9a-21+b = 0

9a+b = 21....(2)

b = 21-9a....(3)

by putting value of b in equation (1)

4a/9+(21-9a) = -14/3

{4a+9(21-9a)}/9 = -14/3

by cross multiplication

3{4a+189-18a} = -14×9

3(-14a+189) = -126

-42a +567 = -126

-42a = -126-567

-42a = -693

a = -693/-42

a = 16.5

by putting value of a in equation 3

b = 21-9(16.5)

b = 21-148.5

b = -127.5

therefore f(x) =

16.5x^2+7x-127.5