Challenge for every Math Enthusiasts

Find the equation of a quadratic polynomial with leading coefficient 1 whose graph passes through the points (4,2) and (6,12).

How many solutions does the given equation has ?

[tex](x^{2} - 2x - 16)^{(x^{2} - 18x + 77)}[/tex] = 0

The sum of all terms of an AP except the first term is -36 and the sum of all terms of the same AP except for the last term is 0, the AP is in decreasing order and the difference between the [tex]10^{th}[/tex] term and [tex]6^{th}[/tex] term is -16. Find the first negative term of the AP.

If [tex]\frac{sin^{4}A}{2} + \frac{cos^{4}A}{3} = \frac{1}{5} [/tex] , then the value of [tex]tan^{2}A[/tex]

A number is chosen at random from the set {1,2,3,……,2000}. Let P be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then find the value of 500P.

Suppose [tex]a, b[/tex] denote the zeroes of the quadratic polynomial [tex]x^{2} + 20x - 2020[/tex] and suppose [tex]c, d[/tex] denote the zeroes of the quadratic polynomial [tex]x^{2} - 20x + 2020[/tex]. The find the value of
[tex]ac(a-c) + ad(a-d) + bc(b-c) + bd(b-d)[/tex]

What is the length of the sides of a triangle with a hypotenuse of [tex]20 cm[/tex] and an area of [tex]96 cm^{2}[/tex].

Find the value of [tex]x[/tex]:
[tex]\sqrt{4x+1} + \sqrt{3x-2} = 1[/tex]

If one root of the quadratic equation [tex]ax^{2} + bx + c = 0[/tex] , where [tex]a\ne0[/tex] and [tex]a[/tex] is a positive integer , is [tex]5 + \sqrt{17} [/tex] . The find the value of [tex](a+b+c)[/tex] given that the [tex]HCF(a,b,c)[/tex] is [tex]3[/tex].

Find the largest four-digit number that is divisible by first 10 natural numbers.