Find all the zeros of the following function
f(x)=x^4+24x^2-25
Answers
Answered by
2
x^4+24x^2-25=0
=>x^4+25x^2-x^2-25=0
=>(x^4+25x^2)-(x^2+25)=0
=>x^2(x^2+25)-(x^2+25)=0
=>(x^2-1)(x^2+25)=0
=>x^2=1,-25
=>x=1,-1,5i,-5i (last two roots are for class 11 student, otherwise ignore)
Mark me brainliest.
=>x^4+25x^2-x^2-25=0
=>(x^4+25x^2)-(x^2+25)=0
=>x^2(x^2+25)-(x^2+25)=0
=>(x^2-1)(x^2+25)=0
=>x^2=1,-25
=>x=1,-1,5i,-5i (last two roots are for class 11 student, otherwise ignore)
Mark me brainliest.
Answered by
0
Answer:
x = 1 or 5
Step-by-step explanation:
x⁴ + 24x² - 25
= (x²)² + 24(x²) - 25 ___(1)
Let y = x², then
= y² + 24y - 25
= y² - 1y + 25y - 25
= y(y - 1) + 25(y - 1)
= (y - 1)(y + 25)_______(2)
From (1) and (2), we get:
(x² - 1)(x² + 25)
To find roots, remainder = 0, therefore:
(x² - 1)(x² + 25) = 0
:. x² = 1, x = 1
or x² = -25, x = +-5
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