Question

If two roots of the equation $(a-1)(x^2+x+1)^2-(a+1)(x^4+x^2+1)=0$ are real and distinct, then find the interval in which $a$ lies

score 8.1k · Answer 1 · 2026-03-26 08:02:21

8.1k

Views

If two roots of the equation $(a-1)(x^2+x+1)^2-(a+1)(x^4+x^2+1)=0$ are real and distinct, then find the interval in which $a$ lies

Published on 26 Mar 2026 - 8:02

score 2k · Answer 2 · 2016-12-31 05:01:36

$\alpha, \beta$ are the roots of $x^2-6(t^2-2t+2)x-2=0$ and $a_n=\alpha^n-\beta^n$ for $n\geq 1$, then find $\frac{a_{100}-2a_{98}}{a_{99}}$

score 13.1k · Answer 3 · 2016-12-31 05:57:43

13.1k

Views

Let $P(x)=4x^2+6x+4$ and $Q(x) =4y^2-12y+25$. If $x,y$ satisfy the equation $P(x)Q(y)=28$, then find the value of $11y-26x$.

Published on 31 Dec 2016 - 5:57

score 581 · Answer 4 · 2026-03-29 12:41:20

581

Views

Conditions for $x^2 + ax - a$ to be a perfect square.

Published on 29 Mar 2026 - 12:41

score 660 · Answer 5 · 2026-03-25 19:07:10

660

Views

Find the Julia set of $f(z) = z^2$ - which sequences of iterates do we need to investigate?

Published on 25 Mar 2026 - 19:07

score 190 · Answer 6 · 2026-03-25 19:05:10

190

Views

From where do we get $\varphi(w) = w + \frac 1 w$ for $w^2$ and $z^2 - 2$?

Published on 25 Mar 2026 - 19:05

score 4.7k · Answer 7 · 2026-03-29 04:33:52

4.7k

Views

Solve $(x-2)^6+(x-4)^6=64$ using a substitution.

Published on 29 Mar 2026 - 4:33

score 163 · Answer 8 · 2017-01-02 00:38:26

163

Views

Show that that $a>\frac{3}{4}$

Published on 02 Jan 2017 - 0:38

score 120 · Answer 9 · 2017-01-02 05:37:26

120

Views

complex coefficient in quadratic equation question

Published on 02 Jan 2017 - 5:37

score 248 · Answer 10 · 2026-03-28 00:05:53

248

Views

Find positive integer solutions of the Diophantine equation $x^4+py^4=z^2$.

Published on 28 Mar 2026 - 0:05

score 87 · Answer 11 · 2017-01-02 15:31:19

87

Views

Is there a general formula for a quadratic that is always positive?

Published on 02 Jan 2017 - 15:31

score 62 · Answer 12 · 2017-01-02 20:41:23

62

Views

Minimum value of a+b+c

Published on 02 Jan 2017 - 20:41

score 496 · Answer 13 · 2017-01-03 13:55:55

496

Views

Level calculation based on total experience points

Published on 03 Jan 2017 - 13:55

score 1.4k · Answer 14 · 2017-01-05 10:44:07

1.4k

Views

Quadratic equation system $A^2 + B^2 = 5$ and $AB = 2$

Published on 05 Jan 2017 - 10:44

score 38.2k · Answer 15 · 2017-01-05 17:01:23

38.2k

Views

How to find a when the quadratic equation has equal roots?

Published on 05 Jan 2017 - 17:01

List Question

If two roots of the equation $(a-1)(x^2+x+1)^2-(a+1)(x^4+x^2+1)=0$ are real and distinct, then find the interval in which $a$ lies

$\alpha, \beta$ are the roots of $x^2-6(t^2-2t+2)x-2=0$ and $a_n=\alpha^n-\beta^n$ for $n\geq 1$, then find $\frac{a_{100}-2a_{98}}{a_{99}}$

Let $P(x)=4x^2+6x+4$ and $Q(x) =4y^2-12y+25$. If $x,y$ satisfy the equation $P(x)Q(y)=28$, then find the value of $11y-26x$.

Conditions for $x^2 + ax - a$ to be a perfect square.

Find the Julia set of $f(z) = z^2$ - which sequences of iterates do we need to investigate?

From where do we get $\varphi(w) = w + \frac 1 w$ for $w^2$ and $z^2 - 2$?

Solve $(x-2)^6+(x-4)^6=64$ using a substitution.

Show that that $a>\frac{3}{4}$

complex coefficient in quadratic equation question

Find positive integer solutions of the Diophantine equation $x^4+py^4=z^2$.

Is there a general formula for a quadratic that is always positive?

Minimum value of a+b+c

Level calculation based on total experience points

Quadratic equation system $A^2 + B^2 = 5$ and $AB = 2$

How to find a when the quadratic equation has equal roots?

Trending Questions

Popular # Hahtags

Popular Questions