Find the square root of x^4-8x^3+mx^2+nx+16 and also find the value of m and n
Answers
Answer:
24 , 32
Step-by-step explanation:
Given
Find the square root of x^4-8x^3+mx^2+nx+16 and also find the value of m and n
Now we need to find square root of the given expression
So x^2 – 4x + (m – 16)/2
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x ^2 x^4 – 8x^3 + mx^2 + nx + 16
2x^2 – 4 x x^4
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- 8x^3 + mx^2
-8x^3 + 16x^4
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2x^2 – 8 x + (m – 16)/2 (m – 16)x^2 + nx + 16
(m – 16)x^2 – 4(m – 16)x + [m – 16/2]^2
Equating the constant term we get
[(m – 16) / 2]^2 = 16
(m – 16)/2 = 4
m – 16 = 8
m = 8 + 16
m = 24
By equating coefficients of x we get
n = - 4(m – 16)
n = -4 (24 – 16)
n = - 4 x 8
n = - 32
So the values of m and n are 24 and - 32
Step-by-step explanation:
Answer is
m = 24
n= -32
I hope this will help you.
