Question Type 5: Finding possible values of parameters given the sum and product of roots Exercises

For the equation $2x^2 + mx + 8 = 0$, the sum of the roots is $5$ and the product is $4$. Find the value of $m$.

For the equation $x^2 + a x + b = 0$, find $a$ and $b$ if the sum of the roots is $7$ and the product is $10$.

For the equation $k x^2 - 6x + b = 0$, the sum of the roots is $3$ and the product is $2$. Find $k$ and $b$.

For the cubic equation $x^3 + bx^2 + 9x + 9 = 0$, the sum of the roots is $2$ and the product is $-9$. Find $b$.

For the cubic equation $x^3 + k x^2 + 4k x - 16 = 0$, if the sum of the roots is $-4$ and the product of the roots is $16$, find $k$.

For the cubic $2x^3 + kx^2 + 7x + 14 = 0$, find $k$ if the sum of the roots is $2$ and the product of the roots is $-7$.

For the equation $x^2 + p x + q = 0$, find $p$ and $q$ if the sum of the roots is $4$ and the product of the roots is $3$.

For the quadratic $3x^2 - px + 6 = 0$, the sum of the roots is $4$ and the product is $2$. Solve for $p$.

For the cubic equation $ax^3 + bx^2 + 5x + 10 = 0$, the sum of the roots is $2$ and the product of the roots is $-10$.

Find $a$ and $b$.

For the cubic $ax^3 + bx^2 + 14x + 21 = 0$, if the sum of the roots is $3$ and the product of the roots is $-7$, find $a$ and $b$.

For the cubic $x^3 - px^2 + 6x - 3p = 0$, the sum of the roots is $4$ and the product of the roots is $12$. Find $p$.

For the cubic equation $k x^3 + 4x^2 + k x + 16 = 0$, the sum of the roots is $-4$ and the product of the roots is $-16$. Determine $k$.