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

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

Similar Questions:

• If one Zero of Polynomial (a^2 + 9) x^2 + 13x + 6a is Reciprocal of other, Find Value of a
• If the Zeros of the Polynomial x²+px+q are Double in Value to the Zeros of 2x²-5x -3, Find the Value of p and q
• If the sum of Zeros of the Quadratic Poynomial p(x) = kx²+2x+3k is Equal to their Product Find the Value of k
• Find the Zeroes of Quadratic Polynomial and Verify the Relationship Between the Zeroes and it’s Coefficient: T^2-15
• If α and β are the Zeros of the Polynomial f(x)=x^2+x−2, Find the Value of (1/α−1/β)
• α, β and γ are the Zeroes of Cubic Polynomial P(x) = ax^3 + bx^2 + cx + d, (a≠0). Then Product of their Zeroes [αβγ] is?
• If the Sum of the Squares of Zeros of Quadratic Polynomial F(X)= x^2 – 8 x + K is 40, Find k
• Find the Zeros of the Following Quadratic Polynomials x²-2x-8 And Verify the Relationship Between the Zeros and the Coefficients
• If One Zero of Polynomial 3x^2-8x+2k+1 in Seven Times other Find the Zero and the Value of the k