Algebraic Equations of Higher Degree

If the roots of a cubic polynomial are $-2, 4, -7$, find the polynomial.

If the roots of a cubic polynomial are $5, 2, 3$, find the polynomial.

The zeros of a polynomial $p\left(x\right)=2x^3+b{x}^2+cx-15$ are $\alpha , \beta , \gamma$. If $\alpha \beta +\beta \gamma +\gamma \alpha =10$ and $\alpha +\beta +\gamma =17$. Find the value of $c$.

If product of roots of bi-quadratic equation $k{x}^4-13x^3+6x^2+36x+14=0$ is $\frac{11}{2}$, then the value of $k$ is 

If sum of roots of bi-quadratic equation $p{x}^4-13x^3+6x^2+36x+14=0$ is $\frac{11}{2}$, then the value of $p$ is 

Write the solutions of the equation: $x^4=13x^2-36$.

Write the solutions of the equation: $x^4-9x^2+20=0$.

Form a cubic equation with roots $2$, $3$, and $-1$

Form a cubic equation with roots $2$, $-3$, and $1$

 The polynomial equation with roots $2$, $-3$, and $1$

 The polynomial equation with roots $2$, $3$, and $-1$

If sum of roots of $4x^4+3k{x}^3+6x^2+7x+8=0$ is $1$, then find the value of $k$.

If the sum of the product of its roots taken two at a time of the bi-quadratic equation $a{x}^4+5x^3+6x^2+7x+8=0$ is $11$, then find the value of $a$.

If product of roots of $a{x}^4+5x^3+6x^2+7x+8=0$ is $7$, then find the value of $a$.

If sum of roots of $4x^4+3k{x}^3+6x^2+7x+8=0$ is $1$, then find the value of $k$.

Find the two consecutive odd natural numbers, the sum of whose squares is $130$.

Find two consecutive odd positive integers, the sum of whose square is $290$.

Find two consecutive positive odd numbers, the sum of whose squares is $74.$

Find two consecutive natural numbers, the sum of whose squares is $181$.

Find two numbers whose sum is $27$ and the product is $182$.