Question

21. For a quadratic polynomial p(x) = x^2- 8x + 15 for all x belongs to r , which one
the following can be true?
(A) P(x) > 0, when 3 < x < 5 and p(x) < 0, when x < 3 or x 25
(B) p(x) > 0, when - 3<xS-5 and p(x) < 0, when x <-3 or x 2-5
(C) p(x) > 0, when x 5 3 or x > 5 and p(x) < 0, when 3 < x < 5
(D) p(x) > 0, when x < - 3 or x>-5 and p(x) < 0, when - 5 <x<-3
(E) None of these
pls answer fast
If you answer I will mark it as brainliest answer

Answer 1

Answer:

Most easy way is graph and answer

Information needed for graph

${x}^{2} - 8x + 15 = 0 \\ {x}^{2} - 3x - 5x + 15 = 0 \\ (x - 3)(x - 5) = 0 \\ x = 3 \: \: \: \: and \: \: \: \: 5$

If in quadratic

$a {x}^{2} + bx + c$

a > 0 , then it is concave upward .

Now observe graph

for 3<x<5 , P(x) < 0 and else P(x) > 0

which is

Option C