188k views
2 votes
Write the quadratic equation whose roots are -4 and 6 and whose leading coefficient is 3​

User Shiraz
by
8.1k points

2 Answers

3 votes

3x²-6x-72. The quadratic equation whose roots are -4 and 6 with a leading coefficient of 3 is 3x²-6x-72.

The solutions of a quadratic equation are x = -4 and x = 6 with a leading coefficient of 3. The solutions are two real numbers which means that (x + 4) and (x - 6) are the factors of our unknown quadratic equation and the leading coefficient is 3.


3(x+4)(x-6)=0

Expand (x+4)(x-6):


3(x^(2) -2x-24)=0\\3x^(2) -6x-72=0 which is our quadratic equation.

User Grouchal
by
6.9k points
6 votes

Answer:

y = 3x² - 6x - 72

Explanation:

Since the roots are x = - 4 and x = 6 then the factors are

(x + 4) and (x - 6) and the quadratic function is

y = a(x + 4)(x - 6) ← a is a multiplier, in this case 3, so

y = 3(x + 4)(x - 6) ← expand factors and distribute by 3

y = 3(x² - 2x - 24)

y = 3x² - 6x - 72

User Qi Luo
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories