Answered

IDNLearn.com is the perfect place to get detailed and accurate answers to your questions. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.

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

Sagot :

Given:

The roots of a quadratic equation are 6 and 2.

Explanation:

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

[tex](x-6)\text{ and (x}-2)[/tex]

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

[tex]\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}[/tex]

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

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

So answer is,

[tex]5x^2-40x+60=0[/tex]

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.