  # If x=2/3 and x=−3 are the Roots of the Quadratic Equation ax²+7x+b=0 then Find the Values of a and b

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Updated on: October 17th, 2023 If x=2/3 and x=−3 are the roots of the quadratic equation ax²+7x+b=0 then find the values of a and b

To solve the given question and to find the values of a and b, we will use the given steps:

• Step 1: Use the given values to find out the exact polynomial: x=2/3 and x=−3
• Step 2: Solve the resulted equation
• Step 3: Compare with the given polynomial ax²+7x+b=0 and find out the values of a and b

Table of content ## If x=2/3 and x=−3 are the Roots of the Quadratic Equation ax²+7x+b=0 then Find the Values of a and b.

Solution:

As given, x=2/3, and x=−3 are roots of the equation ax²+7x+b=0 then

We can use these to find the exact polynomial in the following way: (x−2/3)(x−(−3)=0

On expanding, we will get:

⇒x²−(2/3)x+3x−2=0

⇒x²+(7/3)x−2=0

⇒3x²+7x−6=0

Now we will compare with the given polynomial with two unknown variables: ax²+7x+b=0

Therefore, we will get a=3, b=−6

## If x=2/3 and x=−3 are the Roots of the Quadratic Equation ax²+7x+b=0 then the Values of a = 3, and b = −6

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