IB Mathematics Analysis and Approaches 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 $x^2+ax+b=0$, 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 $x^3+b{x}^2+9x+9=0$, the sum of the roots is $2$ and the product is $-9$. Find $b$.

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

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

For the equation $x^2+px+q=0$, 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 $a{x}^3+b{x}^2+5x+10=0$, the sum of the roots is $2$ and the product of the roots is $-10$.

Find $a$ and $b$.

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

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

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