Multiple choice

If one root of the equation $ax^2+bx+c=0$ is three times the other, then

  1. $3b^2=4ac$
  2. $9b^2=25ac$
  3. $3b^2=16ac$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Roots are alpha and 3*alpha. Sum = -b/a = 4*alpha. Product = c/a = 3*alpha^2. alpha = -b/(4a). c/a = 3*(-b/4a)^2 = 3*b^2/(16a^2). c = 3b^2/(16a) => 16ac = 3b^2.

AI explanation

Let the two roots be k and 3k. The sum of the roots is k+3k=4k, which equals -b/a. The product of the roots is k multiplied by 3k, which is 3k^2, equaling c/a. From the sum equation, k=-b/(4a). Squaring this gives k^2=b^2/(16a^2). Substituting this into the product equation yields 3(b^2)/(16a^2)=c/a. Multiplying both sides by 16a^2 results in 3b^2=16ac.

Keep practicing — related questions