If you divide one of the roots of the equation 4x2+bx−27=0 by the other root, the quotient will be −3. Find b.

Question

If you divide one of the roots of the equation 4x²+bx−27=0 by the other root, the quotient will be −3. Find b.

Answer 1

R1/R2 = -3. Thus R1 = -3 x R2.

R1 x R2 = -27 from the equation.

Substituting -3 x R2 for R1 tells us that -3 x R2 * R2 = -27.

Simplifying, get R2 ^2 = -27/-3 = 9, thus R2 = +/- 3

Since one root divided by the other = -3, R1 = +/- (-3) * (-3) = +/- 9

+9/-3 = -3 (OK). +9/+3 = +3 (NO). -9/-3 = +3 (NO). -9 /+3 = -3 (OK)

Let's factor the original equation using 9 and -3 as roots to get (2x +9) x (2x - 3) = 4x^2 -6x + 18x -27 = 4X^2 +12X -27.

The roots are +9 and -3, and b=12.

If you tried -9 and +3 as roots, then b = -12