Question

Write the quadratic equation whose roots are -1 and -5 , and whose leading coefficient is 2 . (Use the letter to represent the variable.)

Answer 1

`2x^2+12x+10=0`

Explanation:

When you have the roots r1, r2 and the leading coefficient a of a quadratic equation, its factorization is

a(x - r1)(x - r2)

and the quadratic equation would be

a(x - r1)(x - r2) = 0

In this case r1 = -1, r2 = -5 and a = 2, so the quadratic equation is

`\large 2(x-(-1))(x-(-5))=0\Rightarrow 2(x+1)(x+5)=0\Rightarrow\\\\\Rightarrow2(x^2+5x+x+5)=0\Rightarrow2(x^2+6x+5)=0\Rightarrow\\\\\boxed{2x^2+12x+10=0}`