Question

If $P(x)=ax^2+bx+c$ and $Q(x)=-ax^2+dx+c$, $ac$is not $0$, then prove that $P(x)\cdot Q(x)=0$ has at least 2 real roots.

score 631 · Answer 1 · 2026-04-06 00:50:40

631

Views

If $P(x)=ax^2+bx+c$ and $Q(x)=-ax^2+dx+c$, $ac$is not $0$, then prove that $P(x)\cdot Q(x)=0$ has at least 2 real roots.

Published on 06 Apr 2026 - 0:50

score 103 · Answer 2 · 2026-04-11 23:38:03

103

Views

How can I know the number of roots of a pseudo-polynomial?

Published on 11 Apr 2026 - 23:38

score 51 · Answer 3 · 2026-04-12 00:17:25

51

Views

multiplicity of zeros for polynom

Published on 12 Apr 2026 - 0:17

score 49 · Answer 4 · 2026-04-11 08:27:38

49

Views

Zero points of a non-linear function

Published on 11 Apr 2026 - 8:27

score 78 · Answer 5 · 2016-12-21 10:34:44

78

Views

Find polynomials whose sum has specific roots

Published on 21 Dec 2016 - 10:34

score 89 · Answer 6 · 2016-12-21 17:46:22

89

Views

Given polynomial $x^3+3x^2-7x+1$, and its roots $x_1$, $x_2$, $x_3$. what is $x_1^2+x_2^2+x_3^2$

Published on 21 Dec 2016 - 17:46

score 82 · Answer 7 · 2026-03-26 09:37:15

82

Views

Solve for $x$ (both 2 values as plotted on graph):

Published on 26 Mar 2026 - 9:37

score 520 · Answer 8 · 2016-12-23 06:04:20

520

Views

If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.

Published on 23 Dec 2016 - 6:04

score 194 · Answer 9 · 2016-12-23 13:23:16

194

Views

How to solve $x+x^2+x^3+x^4+x^5=62$?

Published on 23 Dec 2016 - 13:23

score 158 · Answer 10 · 2026-04-10 11:14:59

158

Views

How to get minimum and maximum of function with complementary error function

Published on 10 Apr 2026 - 11:14

score 562 · Answer 11 · 2026-04-10 12:36:47

562

Views

$N$th root - real meaning when $N$ is not a decimal

Published on 10 Apr 2026 - 12:36

score 196 · Answer 12 · 2016-12-26 17:01:54

196

Views

Number of real roots of $x^3+9x^2-49x+49=0$

Published on 26 Dec 2016 - 17:01

score 1.2k · Answer 13 · 2026-04-12 19:39:06

1.2k

Views

Generalizing the Rational Roots Theorem to complex rational roots

Published on 12 Apr 2026 - 19:39

score 341 · Answer 14 · 2026-04-12 13:15:25

341

Views

Prove statement about the roots of a monic polynomial, possibly using Rouché?

Published on 12 Apr 2026 - 13:15

score 1.1k · Answer 15 · 2026-04-11 07:13:43

1.1k

Views

Does the square root of $2$ exist?

Published on 11 Apr 2026 - 7:13

List Question

If $P(x)=ax^2+bx+c$ and $Q(x)=-ax^2+dx+c$, $ac$is not $0$, then prove that $P(x)\cdot Q(x)=0$ has at least 2 real roots.

How can I know the number of roots of a pseudo-polynomial?

multiplicity of zeros for polynom

Zero points of a non-linear function

Find polynomials whose sum has specific roots

Given polynomial $x^3+3x^2-7x+1$, and its roots $x_1$, $x_2$, $x_3$. what is $x_1^2+x_2^2+x_3^2$

Solve for $x$ (both 2 values as plotted on graph):

If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.

How to solve $x+x^2+x^3+x^4+x^5=62$?

How to get minimum and maximum of function with complementary error function

$N$th root - real meaning when $N$ is not a decimal

Number of real roots of $x^3+9x^2-49x+49=0$

Generalizing the Rational Roots Theorem to complex rational roots

Prove statement about the roots of a monic polynomial, possibly using Rouché?

Does the square root of $2$ exist?

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