Question

If $x\in R$ and the roots of $ax^2+bx+c=0$ are complex, then the sign of $a^2x^2+abx+ac$ is

score 42 · Answer 1 · 2019-11-05 15:10:36

42

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If $x\in R$ and the roots of $ax^2+bx+c=0$ are complex, then the sign of $a^2x^2+abx+ac$ is

Published on 05 Nov 2019 - 15:10

score 58 · Answer 2 · 2019-11-05 17:39:10

58

Views

Does the equation $5{\sqrt{6x^2-19x-20}}+\frac{1}{4}{\sqrt{4(x^2+1)-17x}}=0$ have any real solutions?

Published on 05 Nov 2019 - 17:39

score 84 · Answer 3 · 2019-11-05 19:02:22

84

Views

How to find a square root

Published on 05 Nov 2019 - 19:02

score 48 · Answer 4 · 2019-11-05 23:36:17

48

Views

Please help solving the equation $(2x+1)^2-3(x+1)^2=0$

Published on 05 Nov 2019 - 23:36

score 3k · Answer 5 · 2019-11-08 01:53:12

3k

Views

Find the domain and range of $f(x)=\log_3(5+4x-x^2)$

Published on 08 Nov 2019 - 1:53

score 51 · Answer 6 · 2019-11-09 18:33:45

51

Views

$a,b,c,d$ are Distinct reals Find $b+d$

Published on 09 Nov 2019 - 18:33

score 137 · Answer 7 · 2026-03-29 10:48:58

137

Views

how to solve $\frac{\sin^2(\theta)-3\cos^2(\theta)+1}{\sin^2(\theta)-\cos^2(\theta)}\equiv2$ and similar equations

Published on 29 Mar 2026 - 10:48

score 43 · Answer 8 · 2026-03-27 00:54:52

43

Views

Solve system solutions

Published on 27 Mar 2026 - 0:54

score 38 · Answer 9 · 2026-03-27 18:08:20

38

Views

Finding the equation of the trajectory

Published on 27 Mar 2026 - 18:08

score 59 · Answer 10 · 2019-11-11 16:47:43

59

Views

transformation of 1st-order ODE to quadratic 1st order ODE

Published on 11 Nov 2019 - 16:47

score 102 · Answer 11 · 2019-11-11 22:57:43

Equations $x^2+bx+ca=0$ and $x^2+cx+ab=0$ have a common root. Prove that equation $x^2+ax+bc=0$ contains two other roots

score 291 · Answer 12 · 2019-11-11 23:54:16

291

Views

Finding a parabola with vertex $(b, a)$ if the vertex of the parabola $y=3x^2-12x+9$ is $(a,b)$

Published on 11 Nov 2019 - 23:54

score 534 · Answer 13 · 2019-11-12 08:31:11

534

Views

If a,b are positive real numbers such that $a-b=2$, then find the smallest value of the constant L for which following satisifies

Published on 12 Nov 2019 - 8:31

score 55 · Answer 14 · 2019-11-12 10:47:31

55

Views

Find the equation which roots are $\alpha, -\beta$ if $\alpha, \beta$ be the roots of $ax^2+bx+c=0$.

Published on 12 Nov 2019 - 10:47

score 37 · Answer 15 · 2019-11-12 13:08:32

37

Views

The number of real roots of the equation

Published on 12 Nov 2019 - 13:08

List Question

If $x\in R$ and the roots of $ax^2+bx+c=0$ are complex, then the sign of $a^2x^2+abx+ac$ is

Does the equation $5{\sqrt{6x^2-19x-20}}+\frac{1}{4}{\sqrt{4(x^2+1)-17x}}=0$ have any real solutions?

How to find a square root

Please help solving the equation $(2x+1)^2-3(x+1)^2=0$

Find the domain and range of $f(x)=\log_3(5+4x-x^2)$

$a,b,c,d$ are Distinct reals Find $b+d$

how to solve $\frac{\sin^2(\theta)-3\cos^2(\theta)+1}{\sin^2(\theta)-\cos^2(\theta)}\equiv2$ and similar equations

Solve system solutions

Finding the equation of the trajectory

transformation of 1st-order ODE to quadratic 1st order ODE

Equations $x^2+bx+ca=0$ and $x^2+cx+ab=0$ have a common root. Prove that equation $x^2+ax+bc=0$ contains two other roots

Finding a parabola with vertex $(b, a)$ if the vertex of the parabola $y=3x^2-12x+9$ is $(a,b)$

If a,b are positive real numbers such that $a-b=2$, then find the smallest value of the constant L for which following satisifies

Find the equation which roots are $\alpha, -\beta$ if $\alpha, \beta$ be the roots of $ax^2+bx+c=0$.

The number of real roots of the equation

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