Q11,12,13 how to solve this type of ques:
 
11. f(x) = ax2 + bx + c where a 0. How many positive real roots does f(x) = 0 have if the maximum value of f(x) occurs at a root?
(1) 0              (2) 1        (3) 2           (4) Either (1) or (2) 
(5)  Either (2) or (3) 



12. f(x) = ax2 + bx + c where a 0. How many positive real roots does f(x) = 0 have if f(x) = 0 has integral roots and the minimum-value-of f(x) is-2 at x = 0.5? 

(1) 0              (2) 1        (3) 2           (4) Either (1) or (2) 
(5)  Either (2) or (3) 


13. The equation ax2 + bx + c = 0, where a, b, c are real numbers, has one root greater than 2 and the other root less than zero. Which of the following is necessarily true? 

(1) a(a + b + c) > 0 
(2) a(a + b + c) < 0 
(3) a+b+c > 0
(4) a+b+c <0




 

Dear student,

13.fx=ax2+bx+c   let roots α,βthen  α>2  and β<0i.for  a>0then using α>2  and β<0f1=a+b+c<0    .....alwaysthen aa+b+c<0   ii.for a<0then using α>2  and β<0f1=a+b+c>0    .....alwaysthen aa+b+c<0   answer   aa+b+c<0  for all case 
Regards

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Shs
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WHAT IS THE MEANING OF CL
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WHAT IS THE MEANING OF SHS
 
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SHS
 
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Shs where it is written
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substitute the respective value in the equation and apply the rule for increasing and decreasing functions 
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