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Tom [10]
3 years ago
12

The vertices of a triangle are located on a coordinate grid as follows: A (2,2) ,B (2,-6) , and C (-5,-6) . What is the area of

ABC ? A. 6 square units B. 12 square units C. 28 square units D. 56 square units
Mathematics
1 answer:
inn [45]3 years ago
3 0
The answer for this question will be c. 28 square units.
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Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 2-√6 , 2+ √6
horsena [70]

Answer:

x^{4} -18x^{3}+104x^{2} -172x-100

Step-by-step explanation:

The 3 roots are given out of which 2 are real and 1 is imaginary. For a polynomial of least degree having real coefficients, it must have a complex conjugate root as the 4th root. Therefore, based on 4 roots, the least degree of polynomial will be 4. Finding the polynomial having leading coefficient=1 and solving it based on multiplication of 2 quadratic polynomials, we get:  

\\\\x_{1} = 2-\sqrt{6} \\x_{2} = 2+\sqrt{6} \\x_{3}=7-i \\x_{4}=7+i \\\\P(x)=1(x-x_{1})(x-x_{2} )(x-x_{3} )(x-x_{4} ) \\\\=(x-(2-\sqrt{6}))(  x-(2+\sqrt{6} )) (x-(7-i))( x-(7+i))\\=((x-2)+\sqrt{6})( ( x-2)-\sqrt{6} ) ((x-7)+i)( (x-7)-i)\\=((x-2)^{2} -(\sqrt{6} )^{2} )((x-7)^{2}-(i)^{2})\\=(x^{2} -4x-2)(x^{2} -14x+50)\\=x^{4} -18x^{3}+104x^{2} -172x-100\\

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3 years ago
Kayla had m marbles. She gave 4 marbles to her cousin. Enter an expression to represent the number of marbles Kayla has now.
Arte-miy333 [17]

Answer:

m-4\\

Step-by-step explanation:

m-4

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