the sum of −2x2 + x + 31 and 3x2 + 7x − 8 can be written in the form ax2 + bx + c, where a, b, and c are constants. What is the
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Answer:
x = 3 + √6 ; x = 3 - √6 ; ;
Step-by-step explanation:
Relation given in the question:
(x² − 6x +3)(2x² − 4x − 7) = 0
Now,
for the above relation to be true the following condition must be followed:
Either (x² − 6x +3) = 0 ............(1)
or
(2x² − 4x − 7) = 0 ..........(2)
now considering the equation (1)
(x² − 6x +3) = 0
the roots can be found out as:
for the equation ax² + bx + c = 0
thus,
the roots are
or
or
and, x =
or
and, x =
or
x = 3 + √6 and x = 3 - √6
similarly for (2x² − 4x − 7) = 0.
we have
the roots are
or
or
and, x =
or
and, x =
or
and, x =
or
and,
Hence, the possible roots are
x = 3 + √6 ; x = 3 - √6 ; ;
Check the picture below.
includes 2, notice, it doesn't go below 2 over the y-axis, and then it keeps on going up. So, the range is from +2 onwards.
includes 2, notice, it doesn't go below 2 over the y-axis, and then it keeps on going up. So, the range is from +2 onwards.