# Math

posted by Majek

Given that the equation x(x-2p)=q(x-p) has real roots for all real values of p and q. If q=3, find a non-zero value for p so that the roots are rational.

1. Steve

x(x-2p)=3(x-p)
x^2-2px = 3x-3p
x^2-(2p+3) + 3p = 0

for rational roots, the discriminant must be a perfect square. That is,

(2p+3)^2-12p
= 4p^2+12p+9-12p
= 4p^2+9
must be a perfect square.
p=2 is one solution

check:
x(x-4) = 3(x-2)
x^2-7x+6 = 0
(x-1)(x-6) = 0
Not only rational, but integers!

## Similar Questions

1. ### math

Having a lil problem Prove that the roots of ax^2 + (a + b)x+b are real for all values of k note the "x"s aren't multiplication signs. a x^2 + bx + c has the discriminant of D = b^2 - 4ac. If D is nonnegative then the function has …
2. ### algebra

Determine the value(s) of k for which x^2+(k-2)x-2k=0 has equal and real roots. a x^2 + bx + c = 0 has two different roots if the discriminant D defined as: D = b^2 - 4 a c does not equal zero. If D = 0 then there is one root. That …

Use the value of the discriminant to determine the number and type of roots for the equation: (x^2+20=12x-16) 1 real, irrational 2 real, rational no real 1 real, rational
4. ### Algebra II

Which describes the number and type of roots of the equation x^2 -625=0?
5. ### Precalculus

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary …
6. ### Math

Determine for what value(s) of d the quadratic equation 5x^2-10x+d = 0 has i) real and distinct roots ii)real and equal roots iii)non-real roots This is what I did to solve for A. 5x^2-10x+d = 0 b^2-4ac = 0 (-10)^2-4(5)(d) = 0 100-20d …
7. ### Pre-Calc/Trig...

Helpp needed, this is sort of confusing me. Describe the nature of the roots for this equation. 2x^2-x+1=0 A. Two real, rational roots B. Two real, irrational roots C. One real, double root D. Two complex roots
8. ### algebra

if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have?
9. ### Pre Cal

Use Descartesâ€™ Rule of Signs to find the number of possible positive, negative, and nonreal roots for the equation, 4x^3+7x^2+7x+3=0 a. 0 positive, 0 negative, 3 non real roots b. 0 positive, 1 or 3 negative, 0 or 2 non real roots …
10. ### Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with rational …

More Similar Questions