Question

Find a quadratic equation whose roots are -3 and 5

Answer 1

Explanation:

Let the roots be a and b

• a=-3
• b=5

To form a equation the formula is

`\sf x^2-(a+b)x+ab`

`\sf➡ {x}^(2) - ( - 3 + 5)x + ( - 3)5 \\ \sf \: ➡ {x}^(2) - 2x - 15 = 0`

Answer 2

• x² - 2x - 15 = 0

Explanation:

Roots:

• x₁ = -3, x₂ = 5

The equation:

• (x - x₁)(x - x₂) = 0
• (x - (-3))(x - 5) = 0
• (x + 3)(x - 5) = 0
• x² + 3x - 5x - 15 = 0
• x² - 2x - 15 = 0