factor 2k^2+k-10 — step-by-step solution

Let's factor in

ℝ

2 k^{2} + k - 10

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 1 - 4 \cdot 2 \cdot (-10)

Δ = 1 + 8 \cdot 10

Δ = 1 + 80

Δ = 81

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

k1 = \frac{- 1 - \sqrt{81}}{2 \cdot 2}

ℹ

- \sqrt{81}

-9

‖

2 \cdot 2

4

k1 = \frac{- 1 - 9}{4}

k1 = - \frac{10}{4}

k1 = - \frac{5}{2}

Solution 2nd:

\frac{- b + \sqrt{Δ}}{2 a}

k2 = \frac{- 1 + \sqrt{81}}{2 \cdot 2}

ℹ

\sqrt{81}

9

‖

2 \cdot 2

4

k2 = \frac{- 1 + 9}{4}

k2 = \frac{8}{4}

k2 = 2

▶Factors identified:

2 \cdot (k - 2) \cdot (k + \frac{5}{2})