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MTLE Mathematics (054, 055) Practice Tests & Test Prep by Exam Edge


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MTLE Mathematics (5-12) Sample Test

1 of 5

Find exact values of a and b, if a + i is a root of the equation

x2 + 3x + b = 0.
Correct Answer:
a = -3/2, b = 13/4


if a + i is a root of the equation x2 + 3x + b = 0 then it should satisfy the equation.

that is (a + i)2 + 3(a + i) + b = 0

after simplifying we will get

a2 + i2 +2ai + 3a + 3i + b = 0

we know that i2  = -1

therefore, a2 - 1 +2ai + 3a + 3i + b = 0

we can write it as

a2 - 1 + 3a + b  +2ai + 3i = 0

or a2 - 1 + 3a + b  +(2a + 3)i = 0

by equating real and imaginary parts to 0, we will get

a2 - 1 + 3a + b = 0  and 2a + 3 = 0

2a + 3 = 0 gives a = -3/2

substitute the value of a into a2 - 1 + 3a + b =0 , and we get

9/4 - 1 - 9/2 + b = 0
therefore
9/4 - 4/4 - 18/4 + b = 0
-13/4 + b = 0
-13/4 = -b
which gives b = 13/4

answer: a = -3/2, b = 13/4
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MTLE Mathematics (5-12) Exam Blueprint