ADVANCED EXERCISES - Polynomials and Roots

(1) Solve the following quadratic equations by factoring. 

 (a) x2 - 5kx + 4k2 = 0

 (b) x2 - 10x + 25 - 49t2y2 = 0; solve for x
( Click On HINT To Get Some Help , Click On SOLUTION To See The Answer )

(2) Find all real solution(s) for each of the following equations by using the quadratic formula. (Note: some equations might not have any real solutions.) 

 x2 + x -  = 0
( HINT , SOLUTION )

(3) Find all real solution(s) for each of the following equations by using the quadratic formula. (Note: some equations might not have any real solutions.) 

 (a) 2x2 + x -  = 0

 (b) kx2 + (3 - 2k)x - 6 = 0; solve for x

 (c) (2x + 5)(x - 3) = 6
( HINT , SOLUTION )

(4) When an object is dropped or thrown downward, the distance, in meters, that it falls in t seconds is given by the following formula: 

             
           s = 4.9t2 + vot
In this formula, vo is the initial velocity, in meters per second. Use the above equation to answer the following questions.

(a) An object is dropped 75 m from an airplane. How long does it take for the object to reach the ground?

(b) An object is thrown downward from the plane at an initial velocity of 30 m/sec. How long does it take for the object to reach the ground?

(c) How far will an object fall in 2 sec if it is thrown downward at an inital velocity of 30 m/sec?

( SOLUTION )

(5)Find a quadratic equation with integer coefficients having the following roots: 

	9  5
        ---------
	   16
( HINT , SOLUTION )



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