Question

Proving that $a^2x^2+(b^2+a^2-c^2)x+b^2=0$ has no real roots if $a+b>c$ and $|a-b|<c$ for real $a$, $b$, $c$

score 795 · Answer 1 · 2026-04-22 20:57:27

795

Views

Proving that $a^2x^2+(b^2+a^2-c^2)x+b^2=0$ has no real roots if $a+b>c$ and $|a-b|<c$ for real $a$, $b$, $c$

Published on 22 Apr 2026 - 20:57

score 166 · Answer 2 · 2026-04-13 16:40:17

166

Views

Drawing two perpendicular tangent line from the origin to $y=x^2-2x+a$

Published on 13 Apr 2026 - 16:40

score 65 · Answer 3 · 2026-04-18 11:59:29

Finding all real $a$, $b$, $c$, $d$ such that $a$ and $b$ are distinct roots of $x^2+cx+d=0$, while $c$ and $d$ are the roots of $x^2+ax+b=0$

score 333 · Answer 4 · 2026-04-11 10:55:22

333

Views

How to find stationary points of a multivariate quadratic function?

Published on 11 Apr 2026 - 10:55

score 361 · Answer 5 · 2026-04-15 22:07:07

361

Views

How does one find values of $m$ for which the roots of $2x^2-mx-8=0$ differ by $m-1$

Published on 15 Apr 2026 - 22:07

score 152 · Answer 6 · 2026-04-17 15:25:49

152

Views

Upper bound of a quadratic, given the upper bound of variable

Published on 17 Apr 2026 - 15:25

score 90 · Answer 7 · 2026-04-17 05:10:10

90

Views

Let $f(x)=ax^2+bx+c, a, b, c \in \mathbb R$. Suppose $|f(x)|\le1 \ \forall x\in [0,1]$ then prove that $|a|+|b|+|c|\le17$

Published on 17 Apr 2026 - 5:10

score 1.1k · Answer 8 · 2026-04-16 00:55:09

Let f(x) be a quadratic polynomial satisfying f(2) + f(4) = 0. If unity is one root of f(x) = 0 then find the other root.

score 86 · Answer 9 · 2026-04-11 15:49:28

86

Views

Can this sum of squares be negative?

Published on 11 Apr 2026 - 15:49

score 319 · Answer 10 · 2026-04-13 19:22:14

319

Views

What does the quadratic formula really do?

Published on 13 Apr 2026 - 19:22

score 195 · Answer 11 · 2026-04-13 18:43:53

195

Views

Cubic's derivative

Published on 13 Apr 2026 - 18:43

score 98 · Answer 12 · 2026-04-14 13:55:54

98

Views

What method is required to find out "for what values of k is $4x^2+kx+\frac14$ a perfect square?"

Published on 14 Apr 2026 - 13:55

score 91 · Answer 13 · 2026-04-17 12:24:32

91

Views

Find all $q \in \mathbb{N}$ such that $\frac{q(q+1)}{12}$ is a Perfect square.

Published on 17 Apr 2026 - 12:24

score 94 · Answer 14 · 2026-04-12 21:14:23

94

Views

Problem while solving question related to quadratic equations by some another method

Published on 12 Apr 2026 - 21:14

score 81 · Answer 15 · 2026-04-16 10:45:38

81

Views

System of two quadratics equation, $P(x)$ and $Q(x)$

Published on 16 Apr 2026 - 10:45

List Question

Proving that $a^2x^2+(b^2+a^2-c^2)x+b^2=0$ has no real roots if $a+b>c$ and $|a-b|<c$ for real $a$, $b$, $c$

Drawing two perpendicular tangent line from the origin to $y=x^2-2x+a$

Finding all real $a$, $b$, $c$, $d$ such that $a$ and $b$ are distinct roots of $x^2+cx+d=0$, while $c$ and $d$ are the roots of $x^2+ax+b=0$

How to find stationary points of a multivariate quadratic function?

How does one find values of $m$ for which the roots of $2x^2-mx-8=0$ differ by $m-1$

Upper bound of a quadratic, given the upper bound of variable

Let $f(x)=ax^2+bx+c, a, b, c \in \mathbb R$. Suppose $|f(x)|\le1 \ \forall x\in [0,1]$ then prove that $|a|+|b|+|c|\le17$

Let f(x) be a quadratic polynomial satisfying f(2) + f(4) = 0. If unity is one root of f(x) = 0 then find the other root.

Can this sum of squares be negative?

What does the quadratic formula really do?

Cubic's derivative

What method is required to find out "for what values of k is $4x^2+kx+\frac14$ a perfect square?"

Find all $q \in \mathbb{N}$ such that $\frac{q(q+1)}{12}$ is a Perfect square.

Problem while solving question related to quadratic equations by some another method

System of two quadratics equation, $P(x)$ and $Q(x)$

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