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Consider the graph ofy = f(x) as shown in the following figure. (i) Find the sumof the roots of the equation f (x) = 0. (ii) Find the product of the roots of the equation f(x) = 4. (iii) Find the absolute value of the difference of the roots of theequationf(x) = x+2 . |
Answer» Solution : (i) Roots of theequation f(x) = 0 OCCUR where thegraph of y = f(x) and y = 0 INTERSECT. From the diagram, the points of intersection ofintersectionare x =- 2 and x= 1. HENCE sum of the roots is - 1. (ii) Roots of the equation f(x) = 4 occur where thegraph of y = f(x) and y = 4 intersect. From thediagram, the points of intersection are x =- 3 and x = 2. Hence the PRODUCT of theroots is -6. (iii) Roots of the equation f(x) = x+2 occur where the graph of y = f(x) and y = x+2 intersect. From thediagram, the points of intersection are x =- 2 and x = 2. Hence the difference of the roots is 4. |
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