homeschool girl
Junior Member
- Joined
- Feb 6, 2020
- Messages
- 123
The problem:
"All the roots of
x2+px+q=0are real, where p and q are real numbers. Prove that all the roots of
x2+px+q+(x+a)(2x+p)=0are real, for any real number a."
What I've got so far:
x2+px+q=0 gives the true statement of p2−4q≥0.
We need to prove that x2+px+q+(x+a)(2x+p)=0 has real roots and, se we need to prove the discriminant is non-negative.
writing it in standard form, I got 3x2+(2p+2a)x+ap+q=0 and i got 4a2+(−4p)a+(−4p2−12q) as the discriminant, so the equation that needs to be proven is 4a2+(−4p)a+(−4p2−12q)≥0.
I'm not sure where to go from here except that I think I need to use p2−4q≥0
"All the roots of
x2+px+q=0are real, where p and q are real numbers. Prove that all the roots of
x2+px+q+(x+a)(2x+p)=0are real, for any real number a."
What I've got so far:
x2+px+q=0 gives the true statement of p2−4q≥0.
We need to prove that x2+px+q+(x+a)(2x+p)=0 has real roots and, se we need to prove the discriminant is non-negative.
writing it in standard form, I got 3x2+(2p+2a)x+ap+q=0 and i got 4a2+(−4p)a+(−4p2−12q) as the discriminant, so the equation that needs to be proven is 4a2+(−4p)a+(−4p2−12q)≥0.
I'm not sure where to go from here except that I think I need to use p2−4q≥0