I'm going to go out on a limb and assume that y2 8y c actually means y^2 + 8y + c c = 16 makes a perfect square: (y + 4)^2 = (y+4)*(y+4) = y^2 + 8y + 16
If the discriminant is a perfect square, it makes calculation easy on paper. Otherwise, the only property of the discriminant that matters is whether it is positive, negative or zero.
6.25
26
For example, find √36. Think, what number times itself makes 36? 6 x 6 = 36 or 6^2 = 36 Thus √36 = √6^2 = 6 In this case 36 is a perfect square. Definition: A perfect square is an integer of the form n^2, where n is a positive integer. The perfect squares are 1, 4, 9, 16, 25, 36, 47, 64, 81, ... You can estimate the value of a square root by finding the two perfect square consecutive numbers that the square root must be between. For example, estimate √29. Since 29 is between 25 and 36, √25 = 5 and √36 = 6 Thus, √29 is between 5 and 6. If you want a better estimates for the value of √29, you can use the calculator and round the answer to the nearest thousands. So for √29 the calculator displays 5.385164807, round that to the nearest thousands. Since 1 < 5, then √29 ≈ 5.385 Either use a calculator or tables. The only other way is trial and error; # guess an answer # square it # compare 2 with the figure you are trying to find the square root of # adjust your guessand go back to 2
What value, in place of the question mark, makes the polynomial below a perfect square trinomial?x2 + 12x+ ?
64
64
-12
The answer will depend on what c is!If the trinomial is ax^2 + bx + c then the required value of c is (b^2)/(4a)
144
(b/2)^2= 64
48
There are infinitely many possible answers: c = ±4x + 33
x2 + 22x + 121 to get this divide 22 by 2... then square the answer you get from that 22/2 = 11 112 = 121
I'm going to go out on a limb and assume that y2 8y c actually means y^2 + 8y + c c = 16 makes a perfect square: (y + 4)^2 = (y+4)*(y+4) = y^2 + 8y + 16
55*55 = 3025 or (-55)*(-55) = 3025 which makes 3025 the square of the integers ±55, and thus a perfect square.