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Maxima/Minima Problem

score 413 · Answer 1 · 2026-04-15 21:35:48

413

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Maxima/Minima Problem

Published on 15 Apr 2026 - 21:35

score 2k · Answer 2 · 2026-04-15 00:58:05

2k

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The least value of $4x^2-4ax +a^2-2a+2$ on $[0,2]$ is $3$. What is the integer part of $a$?

Published on 15 Apr 2026 - 0:58

score 169 · Answer 3 · 2026-04-16 08:46:55

169

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For what $x\in[0,2\pi]$ is $\sin x < \cos 2x$

Published on 16 Apr 2026 - 8:46

score 384 · Answer 4 · 2026-04-17 01:02:20

384

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If $ a+b+c=4 ; a^2=b^2+c=6 ; a^3+b^3+c^3=8 $ Then find the value of $a^4+b^4+c^4$

Published on 17 Apr 2026 - 1:02

score 4.6k · Answer 5 · 2026-04-16 19:00:10

Find all values of a for which the equation $x^4 +(a-1)x^3 +x^2 +(a-1)x+1=0$ possesses at least two distinct negative roots

score 4.5k · Answer 6 · 2026-04-17 02:06:21

4.5k

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The no. of values of k for which $(16x^2+12x+39) + k(9x^2 -2x +11)$ is perfect square is:

Published on 17 Apr 2026 - 2:06

score 6.9k · Answer 7 · 2026-04-15 23:17:34

6.9k

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If $ax^2-bx+c=0$ has two distinct real roots lying in the interval $(0,1)$ $a,b,c$ belongs to natural prove that $\log_5 {abc}\geq2$

Published on 15 Apr 2026 - 23:17

score 1.6k · Answer 8 · 2026-04-15 11:41:51

The number of integral values of $a$ for which the inequality $3- |x-a |>x^2$ is satisfied by at least one negative $x$, must be equal to 6

score 1.3k · Answer 9 · 2026-04-16 12:53:35

1.3k

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How to solve problems involving roots. $\sqrt{(x+3)-4\sqrt{x-1}} + \sqrt{(x+8)-6\sqrt{x-1}} =1$

Published on 16 Apr 2026 - 12:53

score 2k · Answer 10 · 2026-04-17 20:22:35

2k

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If $(2x^2-3x+1)(2x^2+5x+1)=9x^2$,then prove that the equation has real roots.

Published on 17 Apr 2026 - 20:22

score 140 · Answer 11 · 2026-04-14 13:20:38

140

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How to search quadratic function

Published on 14 Apr 2026 - 13:20

score 312 · Answer 12 · 2026-04-14 11:27:36

312

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maximum using completing the square

Published on 14 Apr 2026 - 11:27

score 294 · Answer 13 · 2026-04-14 04:57:59

294

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Given that the roots of the quadratic equation $x^2+2ax+3a=0$ lie between $-1$ and $1$, what are the possible values of $a$?

Published on 14 Apr 2026 - 4:57

score 58 · Answer 14 · 2026-04-09 13:47:19

58

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Help with this solution of quadratic equation

Published on 09 Apr 2026 - 13:47

score 681 · Answer 15 · 2026-04-16 13:33:34

681

Views

Determine all the values of the parameter $a$ for which the inequality $3-|x-a|>x^2$ is satisfied by at least one negative $x$.

Published on 16 Apr 2026 - 13:33

List Question

Maxima/Minima Problem

The least value of $4x^2-4ax +a^2-2a+2$ on $[0,2]$ is $3$. What is the integer part of $a$?

For what $x\in[0,2\pi]$ is $\sin x < \cos 2x$

If $ a+b+c=4 ; a^2=b^2+c=6 ; a^3+b^3+c^3=8 $ Then find the value of $a^4+b^4+c^4$

Find all values of a for which the equation $x^4 +(a-1)x^3 +x^2 +(a-1)x+1=0$ possesses at least two distinct negative roots

The no. of values of k for which $(16x^2+12x+39) + k(9x^2 -2x +11)$ is perfect square is:

If $ax^2-bx+c=0$ has two distinct real roots lying in the interval $(0,1)$ $a,b,c$ belongs to natural prove that $\log_5 {abc}\geq2$

The number of integral values of $a$ for which the inequality $3- |x-a |>x^2$ is satisfied by at least one negative $x$, must be equal to 6

How to solve problems involving roots. $\sqrt{(x+3)-4\sqrt{x-1}} + \sqrt{(x+8)-6\sqrt{x-1}} =1$

If $(2x^2-3x+1)(2x^2+5x+1)=9x^2$,then prove that the equation has real roots.

How to search quadratic function

maximum using completing the square

Given that the roots of the quadratic equation $x^2+2ax+3a=0$ lie between $-1$ and $1$, what are the possible values of $a$?

Help with this solution of quadratic equation

Determine all the values of the parameter $a$ for which the inequality $3-|x-a|>x^2$ is satisfied by at least one negative $x$.

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