If all integers satisfying the inequality ((x-1)2(x-2)3(x-4)5(x-5)5/(x-5)2) ≥ 0 are arranged in increasing order then the quadratic equation with the first and fifth integers in the list as roots is

Question

If all integers satisfying the inequality ((x-1)2(x-2)3(x-4)5(x-5)5/(x-5)2) ≥ 0 are arranged in increasing order then the quadratic equation with the first and fifth integers in the list as roots is (A) x2-8 x+12=0 (B) x2-6 x+5=0 (C) x2-5 x+4=0 (D) x2-7 x+6=0

Tardigrade Admin · Accepted Answer

(x-2)3(x-4)5(x-5)3 ≥ 0 ; x=1, x ≠ 5 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e81a93f37e4553d89dbc33ebd978622a-.png" /> x ∈[2,4] ∪(5, ∞) ∪ 1 ⇒ text integers (1), 2,3,4,(6) ldots ldots Equation with roots 1,6 x 2-7 x +6=0

Q. If all integers satisfying the inequality $\frac{( x - 1 ) ^{2} ( x - 2 ) ^{3} ( x - 4 ) ^{5} ( x - 5 ) ^{5}}{( x - 5 ) ^{2}} \geq 0$ are arranged in increasing order then the quadratic equation with the first and fifth integers in the list as roots is

$x^{2} - 8 x + 12 = 0$

$x^{2} - 6 x + 5 = 0$

$x^{2} - 5 x + 4 = 0$

$x^{2} - 7 x + 6 = 0$

$(x - 2)^{3} (x - 4)^{5} (x - 5)^{3} \geq 0; x = 1, x \neq = 5$

$x \in [2, 4] \cup (5, \infty) \cup {1} \Rightarrow integers (1), 2, 3, 4, (6) \dots\dots$
Equation with roots 1,6
$x^{2} - 7 x + 6 = 0$

Q. If all integers satisfying the inequality (x−5)2(x−1)2(x−2)3(x−4)5(x−5)5​≥0 are arranged in increasing order then the quadratic equation with the first and fifth integers in the list as roots is

x2−8x+12=0

x2−6x+5=0

x2−5x+4=0

x2−7x+6=0