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Solving a Quadratic Equation by Factorization Method

If x=2 / 3 an...

Question

If x = 2/3 and x = −3 are the roots of the equation ax² + 7x + b = 0, find the values of a and b.

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Solution

We have been given that,

We have to find a and b

Now, if is a root of the equation, then it should satisfy the equation completely. Therefore we substitute in the above equation. We get,

…… (1)

Also, if is a root of the equation, then it should satisfy the equation completely. Therefore we substitute in the above equation. We get,

…… (2)

Now, we multiply equation (2) by 9 and then subtract equation (1) from it. So we have,

Now, put this value of ‘a’ in equation (2) in order to get the value of ‘b’. So,

Therefore, we have and .

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Similar questions

If $x = \frac{2}{3}$ and x = - 3 are the roots of equation $a x^{2} + 7 x + b = 0,$ find values of a and b.

x = 2

x = - 3

a x^{2} + 7 x + b = 0

a

b

x = \frac{2}{3}

x = - 3

a x^{2} + 7 x + b = 0,

If $x = \frac{2}{3} a n d x = - 3$ are the roots of the quadratic equation $a x^{2} + 7 x + b = 0$ then find the values of a and b.

x = \frac{2}{3}

x = - 3

a x^{2} + 7 x + b = 0,

a^{2} + b^{2}

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