Question

Let f(x) = $x^2+ax+b,a,b \in R$. If $f(1)+f(2)+f(3)=0$, then the nature of the roots of the equation $f(x) =0$ is .....

score 602 · Answer 1 · 2026-04-16 03:56:21

602

Views

Let f(x) = $x^2+ax+b,a,b \in R$. If $f(1)+f(2)+f(3)=0$, then the nature of the roots of the equation $f(x) =0$ is .....

Published on 16 Apr 2026 - 3:56

score 83 · Answer 2 · 2026-04-16 00:53:54

83

Views

Given $x^2 - 3x +6=0$ find $x^4$ in terms of $x$.

Published on 16 Apr 2026 - 0:53

score 747 · Answer 3 · 2026-04-17 12:22:39

747

Views

Question on applying the constraint $x^Tx=1$ in optimization using eigenvalues of quadratic form $x^TAx$

Published on 17 Apr 2026 - 12:22

score 75 · Answer 4 · 2026-04-23 16:40:59

75

Views

Find the meaning of the expression $\sqrt[3]{19 - a} + \sqrt[3]{10 - a}$, if $\sqrt[3]{19 - a} - \sqrt[3]{10 - a} = 1$.

Published on 23 Apr 2026 - 16:40

score 35 · Answer 5 · 2026-04-14 17:55:38

35

Views

What is the value of this Integral? I got it after deriving weber's attractive velocity dependent force.

Published on 14 Apr 2026 - 17:55

score 39 · Answer 6 · 2026-04-11 19:33:25

39

Views

Can we say something about roots of quadatric equation whose coefficient consists of terms that tend to 0?

Published on 11 Apr 2026 - 19:33

score 196 · Answer 7 · 2026-04-17 11:24:25

196

Views

Why am I not able to find the intersection of circles $(x-2)^2+(y-5)^2=5$ and $(x-1)^2+(y+3)^2=50$ algebraically?

Published on 17 Apr 2026 - 11:24

score 71 · Answer 8 · 2026-04-17 15:16:18

71

Views

Finding integer $a$, $b$ such that the roots of $3x^2+3(a+b)x+4ab=0$ satisfy $\alpha(\alpha+1)+\beta(\beta+1)=(\alpha+1)(\beta+1)$

Published on 17 Apr 2026 - 15:16

score 219 · Answer 9 · 2026-04-16 11:59:58

219

Views

Find the limits between which $a$ must lie in order that $\frac{ax^2-7x+5}{5x^2-7x+a}$ can take all real values

Published on 16 Apr 2026 - 11:59

score 330 · Answer 10 · 2026-04-12 15:02:59

330

Views

Translation of parabola in cartesian plane

Published on 12 Apr 2026 - 15:02

score 144 · Answer 11 · 2026-04-16 14:20:49

144

Views

$f(x) = ax^2+bx+c$ are positive, and $a+b+c=1$. Prove $f(x_1)f(x_2)...f(x_n)\geq1$ is true for all positive $x$, satisfying $x_1x_2...x_n=1$

Published on 16 Apr 2026 - 14:20

score 71 · Answer 12 · 2026-04-15 00:26:44

71

Views

If |a|> |a+b+c| prove that there is complex root such that |z|< 2

Published on 15 Apr 2026 - 0:26

score 246 · Answer 13 · 2026-04-12 19:58:41

246

Views

How to find a real function with that has certain imaginary roots

Published on 12 Apr 2026 - 19:58

score 60 · Answer 14 · 2026-04-15 16:16:11

60

Views

Solving the equation $X^2 + (3 +i)X + 1 +i =0$

Published on 15 Apr 2026 - 16:16

score 108 · Answer 15 · 2026-04-17 11:55:47

108

Views

Prove that $ f(f(x)) \geq 0$ for all real x

Published on 17 Apr 2026 - 11:55

List Question

Let f(x) = $x^2+ax+b,a,b \in R$. If $f(1)+f(2)+f(3)=0$, then the nature of the roots of the equation $f(x) =0$ is .....

Given $x^2 - 3x +6=0$ find $x^4$ in terms of $x$.

Question on applying the constraint $x^Tx=1$ in optimization using eigenvalues of quadratic form $x^TAx$

Find the meaning of the expression $\sqrt[3]{19 - a} + \sqrt[3]{10 - a}$, if $\sqrt[3]{19 - a} - \sqrt[3]{10 - a} = 1$.

What is the value of this Integral? I got it after deriving weber's attractive velocity dependent force.

Can we say something about roots of quadatric equation whose coefficient consists of terms that tend to 0?

Why am I not able to find the intersection of circles $(x-2)^2+(y-5)^2=5$ and $(x-1)^2+(y+3)^2=50$ algebraically?

Finding integer $a$, $b$ such that the roots of $3x^2+3(a+b)x+4ab=0$ satisfy $\alpha(\alpha+1)+\beta(\beta+1)=(\alpha+1)(\beta+1)$

Find the limits between which $a$ must lie in order that $\frac{ax^2-7x+5}{5x^2-7x+a}$ can take all real values

Translation of parabola in cartesian plane

$f(x) = ax^2+bx+c$ are positive, and $a+b+c=1$. Prove $f(x_1)f(x_2)...f(x_n)\geq1$ is true for all positive $x$, satisfying $x_1x_2...x_n=1$

If |a|> |a+b+c| prove that there is complex root such that |z|< 2

How to find a real function with that has certain imaginary roots

Solving the equation $X^2 + (3 +i)X + 1 +i =0$

Prove that $ f(f(x)) \geq 0$ for all real x

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