Question

Write the quadratic equation whose roots are 6 and 2 with leading coefficient of 5.

Answer 1

Given:

The roots of a quadratic equation are 6 and 2.

Step-by-step explanation:

The factors of a quadratic with roots 6 and 2 are,

`(x-6)\text{ and (x}-2)`

The quadratic equation can be expressed as product of two factors. So,

`\begin{gathered} (x-6)(x-2)=0 \\ x\cdot x-6\cdot x-2\cdot x-6\cdot(-2)=0 \\ x^2-6x-2x+12=0 \\ x^2-8x+12=0 \end{gathered}`

Since leading coefficient is 5. So multiply the quadratic equation by 5.

`\begin{gathered} 5(x^2-8x+12)=5\cdot0 \\ 5x^2-40x+60=0 \end{gathered}`

So answer is,

`5x^2-40x+60=0`