Question :
Directions :Answer the given set of questions based on the following information:
Equation 1: ax2 - 9x + 7 = 0
Equation 2: by2 - 8y + 4 = 0
Notes:
1) Both a and b are positive integers where b > a.
2) One of the roots of equation 2 is 2/3.
3) The ratio of highest root of equation 1 to the highest root of equation 2 is 7: 4.
Find the value of (a + b).
Solution :
Equation 2:
by2 - 8y + 4 = 0
One of the roots of equation 2 is 2/3. So,
b(2/3)2 - 8(2/3) + 4 = 0
4b/9 = 4/3
b = 3
Now, 3y2 - 8y + 4 = 0
3y2 - 6y - 2y + 4 = 0
3y(y - 2) - 2(y - 2) = 0
(y - 2)(3y - 2) = 0
y = 2, 2/3
The ratio of highest root of equation 1 to the highest root of equation 2 is 7: 4. So,
Highest root of equation 1 = 2 * 7/4 = 7/2
Now, Equation 1: ax2 - 9x + 7 = 0
a(7/2)2 - 9(7/2) + 7 = 0
49a/4 = 49/2
a = 2
So, 2x2 - 9x + 7 = 0
2x2 - 7x - 2x + 7 = 0
x(2x - 7) - 1(2x - 7) = 0
(2x - 7)(x - 1) = 0
x = 7/2, 1
a + b = 3 + 2 = 5
Study Notes
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