If $alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c= 0$ express the roots of the equation $a^3x^2-ab^2x+b^2c=0$ in terms of $\alpha$ and $\beta$ @LeakyNun. I have the solution. I have a doubt in one part of it.
@LeakyNun please tell me one concrete application of Quadratic equations and the problems we solve in real life. It would be okay if you answer in a single line concisely.
$(x-a)(x-12)+13 = 0$ Why is it necessary for $a$ and other coefficients to be rational for the equation to have integral roots? I mean I was told this condition but I can't interpret it's reason @LeakyNun.
@LeakyNun Really sorry for asking so many basic questions :"(. Today I was even scolded by my teacher for asking too many doubts during the class :"(.
@LeakyNun $(a+2b-3c)x^2 + (b+2c-3a)x + (c+2a-3b)=0$ is an equation given as a part of a question. SOlution begins with "as coefficients are cyclic, f(1) = 0"
`prove that the set of values of k for which $18x^2 -6(2k+1) +k(k+1)= 0$ may have one root less than k and othe root greater than k are given by $(0,\frac{5}{7})$
I got $\Delta = 72k^2 +72k +36$ = always positive @LeakyNun (therfore 2 real and distinct roots exist)
`prove that the set of values of k for which $18x^2 -6(2k+1) +k(k+1)= 0$ may have one root less than k and othe root greater than k are given by $(0,\frac{5}{7})$
$18x^2- 6(2k+1)x +k(k+1)= 0$
:39796151 A long circular bracket is given. The one that indicates open interval.
Consider the inequation $x^2 +|x+a|-9<0$. Find the values of the real parameter a so that the given inequation has at least one negative solution @LeakyNun.
