1.

in the given figure y=x^(2)+bx+c is a quadratic polynomial which meets x-axis at A and B and y-axis at C Q is vertex of quadratic polynomial and foot of perpendicular from Q to x-axis and y-axis are P and R respectively. Then answer the following questions. Q. If ("area of" DeltaABC)/("Area of rectangle" OPQR)=(8)/(3) satisfies the relation b^(2)=kc then k will be

Answer»

`9`
`(2)/(9)`
`(9)/(2)`
`2`

Solution :`((1)/(2)(beta-alpha)C)/(((b^(2)-4c)/(4))(-(b)/(2)))=(8)/(3)` squaring and using
`(beta-alpha)^(2)=b^(2)-4c`
`9C^(2)=4b^(4)-16b^(2)c`
`4b^(4)-16b^(2)c-9c^(2)=0`
`4b^(4)-18B^(2)c+2b^(2)c-9c^(2)=0`
`(2b^(2)+c)(2b^(2)-9c)=0impliescgt0because2b^(2)+cne0`
`(b^(2))/(c)=(9)/(2)implies(b^(2))/(c)=4.5`


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