Question

Write the quadratic equation whose roots are 4 and -2 and whose leading coffecient is 2

Answer 1

`y=2x^2-4x-16`

Explanation:

Factored form of a quadratic equation:

`y=a(x-r_1)(x-r_2)`

where:

• a is the leading coefficient
• 
  `r_1` and
  `r_2` are the roots

Given:

• 
  `a = 2`
• 
  `r_1=4`
• 
  `r_2=-2`

Substitute the given values into the formula and expand:

`\implies y=2(x-4)(x-(-2))`

`\implies y=2(x-4)(x+2)`

`\implies y=2(x^2+2x-4x-8)`

`\implies y=2x^2-4x-16`