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Grade 11Algebra

If f(x) = ax2 + bx + c and f(-1) >= -4, f(1) and f(3) >= 5, then the least value of a is
(a) 1/4
(b) 1/8
(c) 1/3
(d) -1/3
Please explain the answer with proper steps.

Profile image of Viraaj Sandip Raulgaonkar
6 Years agoGrade 11
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2 Answers

Profile image of Srutarshi Tripathi
5 Years ago
First of all, You have missed one important information. f(1)  0.
Now, we have
f(-1) > 4
or,a-b+c > 4………(i)
f(1)  0
⇒ a + b + c  0
or, -a-b-c > 0………(ii)(ii)
f(3) > 5
or, 9a+3b+c > 5……….(iii)
From  (i)+(ii) ⇒ -2b > -4……......(iv)
From (ii)+(iii)+(iv), 8a > 1 ⇒ a > 1/8 (ANSWER is B)
Profile image of Srutarshi Tripathi
5 Years ago
First of all, You have missed one important information. f(1)  0.
Now, we have
f(-1) > 4
or,a-b+c > 4………(i)
f(1)  0
⇒ a + b + c  0
or, -a-b-c > 0………(ii)(ii)
f(3) > 5
or, 9a+3b+c > 5……….(iii)
From  (i)+(ii) ⇒ -2b > -4……......(iv)
From (ii)+(iii)+(iv), 8a > 1 ⇒ a > 1/8 (ANSWER is B)

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