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If x=2/3 and x= -3 are …

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If x=2/3 and x= -3 are the roots of the equation ax sauare + 7x + b = 0 find the value of a and b

Posted by Poorvi Gupta 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We have, ax² + 7x + b = 0

Since x = {tex}{2 \over 3}{/tex}, -3 are the solutions of the given equation

Substitute x = {tex}{2 \over 3}{/tex} in the given equation, we get

{tex}a({2 \over 3})^2 + 7({2 \over 3})+b =0{/tex}

{tex}\implies {4a \over 9} + {14 \over 3} + b =0{/tex}

Multiplying the equation by 9, we get

4a + 9b + 42 = 0 ......(i)

Now, substitute x = - 3 in the given equation, we get

a(-3)² + 7 (-3) + b = 0

9a +b - 21 = 0 ........(ii)

Multiplying the equation by 9, we get

81a +9b - 189 = 0 ........(ii)

subtracting(ii) from (i), we get

-77a = -231 or a = 3

Substitue a =3 in (i), we get

4(3) + 9b +42 = 0

{tex}\implies{/tex}9b + 54 = 0 or b = -6

So, a = 3 and b = -6

0Thank You

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