Daily Math Problems — May 26, 2026: Quadratic equations, Analytic Geometry, Sequences

Problems & worked solutions

International

The sum of the roots of $x^{2} - 7 x + 10 = 0$ equals:

Show answer & worked solution

By Viète's formulas, $x_{1} + x_{2} = - (- 7) = 7$ . (The product is $10$ , so the roots are $2$ and $5$ .)

RO M1

The volume of the tetrahedron with vertices $(0, 0, 0), (3, 0, 0), (0, 4, 0), (0, 0, 5)$ is:

Show answer & worked solution

The three edges from origin are $(3, 0, 0), (0, 4, 0), (0, 0, 5)$ . Determinant: $3 \cdot 4 \cdot 5 = 60$ . Volume: $60 / 6 = 10$ .

RO M1

For the geometric progression $1, 2, 4, 8, 16, 32, \dots$ , the sum $b_{2} + b_{4} + b_{6}$ equals:

Show answer & worked solution

$b_{2} = 2$ , $b_{4} = 8$ , $b_{6} = 32$ . The sum is $2 + 8 + 32 = 42$ . (These three form a GP with first term $2$ and ratio $4$ .)

Problems & worked solutions

International

The sum of the roots of $x^{2} - 7 x + 10 = 0$ equals:

Show answer & worked solution

By Viète's formulas, $x_{1} + x_{2} = - (- 7) = 7$ . (The product is $10$ , so the roots are $2$ and $5$ .)

RO M1

The volume of the tetrahedron with vertices $(0, 0, 0), (3, 0, 0), (0, 4, 0), (0, 0, 5)$ is:

Show answer & worked solution

The three edges from origin are $(3, 0, 0), (0, 4, 0), (0, 0, 5)$ . Determinant: $3 \cdot 4 \cdot 5 = 60$ . Volume: $60 / 6 = 10$ .

RO M1

For the geometric progression $1, 2, 4, 8, 16, 32, \dots$ , the sum $b_{2} + b_{4} + b_{6}$ equals:

Show answer & worked solution

$b_{2} = 2$ , $b_{4} = 8$ , $b_{6} = 32$ . The sum is $2 + 8 + 32 = 42$ . (These three form a GP with first term $2$ and ratio $4$ .)